A domain is what a deity has influence over. A god of the deep forests would be considered part of the nature domain, whereas a god with a light domain may focus on rebirth and radiance. Deities can influence multiple domains. The gods of certain domains will be added to the domain section in time.
Clerics chose a Divine Domain to channel their magic at first level. When making a Cleric, consider the temperament of your character and what things they may value. This can help you choose which deity and domain would be best suited for them.
Paladins, too, draw their magic from the gods. At third level, a Paladin must choose a Sacred Oath, a divine promise to follow the path of righteousness in the name of justice and their god.
Druids can also worship nature gods to aid in their connection with the land, but this is not required.
Some other subclasses (the thing you specialize in as you level up) that utilize gods include: Barbarian: Path of the Zealot (level three, your rage allows you to use divine magic, as gifted by a god), a Divine Soul Sorcerer (level three, your magic has been gifted to you by a divine source), and a Warlock whose patron is a Celestial (level one, from making a pact with a Celestial being, your magic has a divine spark to it).
If you would like to worship a specific god as a Cleric or Paladin that doesn't exactly align with 5th Edition rules, talk to your DM and discuss your options! My notes on Paladin Oath suggested gods is just a suggestion, I encourage you to look into various gods until you find one that works best for you and your character's backstory.
Gods that influence the Arcana domain have a keen understanding of magical potential in the multiverse and the importance of esoteric knowledge. Good gods of Arcana may wish for their followers to seek out and protect magical artifacts or secrets; evil gods of Arcana may wish their followers to seek out magical knowledge to better serve their own purposes.
Gods of the Death domain are frequently those that hold power over how death can occur. They also tend to have a connection to the undead or the planes of the afterlife.
Gods of the Forge domain understand that it is through perseverance and hard work that things are accomplished. Often acting as patrons for mortals who work with forges, gods of the Forge domain spark inspiration in their followers in the pursuit of creation through fire.
Gods of the Grave domain act as the watchers of the barrier between life and death. These gods believe that death is a natural part of life and have a firm stance that undead creatures are a disgrace to the natural order. Unlike the Death domain, the Grave domain followers seek to destroy the undead and focus on the transition between life to death.
Gods of the Knowledge domain understand and uphold the power of knowledge. While good deities of the Knowledge domain may seek to spread knowledge throughout the world for the betterment of people, evil gods of Knowledge may collect and hide knowledge from others to gain power for themselves.
Gods of the Life domain see the wonder of life and health and seek to care for the people around them. DNDBeyond notes that "Almost any non-evil deity can claim influence over this domain, particularly agricultural deities, gods of healing or endurance, and gods of home and community" (2020).
Gods of the Light domain seek to destroy darkness and bring hope to all. Sun deities, as well as gods of rebirth, are often a part of this domain.
Gods of the Nature domain deal with the preservation and protection of nature. Good followers of these gods may be focused on preserving the woodlands, while evil followers may encourage plagues upon those who disrespect their god.
Focused on devotion to an idea or place's laws and rules, gods of the Order domain praise logic, discipline, and respect of the established hierarchies. Gods of Order believe that law is the thing that maintains a sense of "security in a chaotic multiverse" (DNDBeyond, 2020). Though this domain was published in Guildmasters' Guide to Ravnica, it was republished for wider distribution in Tasha's Cauldron of Everything, in November of 2020. Deities in books printed before November of 2020 may not have the Order domain as a playable option.
Gods of the Peace domain hold up the virtue of peace, and their followers fight against those that may disrupt that peace. Followers tend to act as mediators and encourage people to work together. This domain was published in Tasha's Cauldron of Everything, which was published in November of 2020. Deities in books printed before November of 2020 may not have the Peace domain as a playable option.
Tempest domain deities oversee the "storms, sea, and sky" (DNDBeyond, 2020). Often as changeable as the weather, these gods have moods that can change in a heartbeat and have their followers encourage sacrifices for protection or enact divine justice.
Gods of the Trickery domain act as instigators and encourage their followers to act as a "disruptive force in the world" (DNDBeyond, 2020). Followers of Trickery domain gods tend to use underhanded tactics to achieve their means.
Gods of the Twilight domain keep watch over the transition from light to dark. Followers of these gods willingly travel into the darkness and seek to make it a safe space for all. This domain was published in Tasha's Cauldron of Everything, which was published in November of 2020. Deities in books printed before November of 2020 may not have the Twilight domain as a playable option.
War domain gods watch over the battles of mortals, inspiring warriors with divine favor. Followers of War domain gods can be as varied as war itself. Followers of the good War domain gods may act in honor and as heroes, whereas followers of an evil War domain god may take relish destruction.
Paladins of this Oath seek glory in battle. Oath of Conquest Paladins tend to worship gods of the War domain.
Paladins of this Oath are the typical picture of the "knight in shining armor, acting with honor in pursuit of justice and the greater good" (DNDBeyond, 2020). Oath of Devotion Paladins tend to worship gods of the Order domain or any god that is good-aligned.
Paladins of this Oath have faith in destiny, believing that glory is destined for them. Oath of Glory Paladins face every challenge with courage and tend to draw on the gods of Theros. This Oath is from the D&D sourcebook The Mythic Odysseys of Theros.
Paladins of this Oath see the path to good for everyone and aim to help wrongdoers find redemption. Oath of Redemption Paladins prefer kindness to violence and only kill if they must. Worship for this Oath tends to be for gods of the Life, Light, and Peace domains.
Paladins of this Oath love the life and beauty of the multiverse and fight to preserve these values, not because they believe in being honorable. Oath of the Ancients Paladins tend to worship gods of the Light, Life, Peace, and Nature domains.
Paladins of this Oath are dedicated to serving civilization and see law and order as the highest form of ruling. Oath of the Crown Paladins are often knights and tend to worship gods of Order and Knowledge.
Paladins of this Oath see the threat that extraplanar creatures, creatures that are not from the material plane (which is where most campaigns take place), pose and train themselves in the pursuit of defending the material plane against these threats. Oath of the Watcher paladins often worship gods of the Light, War, Twilight, and Arcana domains.
Paladins of this Oath deal swift vengeance to the forces of evil, seeing the need for someone to the right the wrongs committed against the innocent. Oath of Vengeance Paladins tend to worship gods of the Order, War, and Tempest domains.
An Oathbreaker is a Paladin whose Sacred Oath has been broken and has betrayed their god. Oathbreaker Paladins are typically on the side of evil, and as such, their abilities reflect that alignment.