Gay is the informal word used over "homosexual" which has been more or less abandoned due to clinical intonations.
Gay typically refers to a man who is romantically or sexually attracted to men.
Gay is used rather broadly, from describing men who are attracted to men, women to women, bi people (although more light heartedly) to even being used as an insult (don't do that).
Lesbian is a more specific term used for women romantically or sexually attracted to other women and is often favoured over "gay".
Both gay and lesbian people are monosexual, that is, they are only attracted to one gender (as compared to multisexual sexualities like bisexual and pansexual).
I have mentioned so many times before but I reiterate that people experiencing same sex attraction are perfect normal and natural. It's extremely similar to straight people experiencing attraction to the opposite gender, only with the door swinging the other way and with the bonus hatred and discrimination.
Interestingly, various studies show that homosexuality is a biological trait as, in a pair of twins, the "second" one was more likely to be gay if the "first" was also gay. This further negates the idea that being gay is a "choice" or is "unnatural". I mean, already given the fact that 15,000+ species do demonstrate homosexuality, it is kind of hard to still suggest it's unnatural.
Honestly, there is not much to be talked about concerning gay and lesbian people - I have talked a lot about this before.