Mood is a category applied to verbs. This allows a speaker to express their attitude toward what they are saying (for example, whether it is intended as a statement of fact, of desire, of command, etc.). Much more detail in GGBB p. 442ff. Most verbs are in the indicative mood which is the mood of simple declaration or question:
The subjunctive mood implies possibility or potential. In English, use a helping verb like “might” or “would”.
Verbs in the imperative mood give a command.
There are four moods that correspond more or less to their English counterparts: indicative, subjunctive, optative, imperative.
The imperative mood gives a command. See BBG chapter 33 or the paradigm below.
The subjunctive mood is a verb mood typically used in dependent clauses to express wishes, commands, emotion, possibility, judgment, opinion, necessity, or statements that are contrary to fact at present. (BBG chp. 31) See also principle 27.
The optative mood is a mood that indicates a wish or hope. It is similar to the cohortative in Hebrew, and closely related to the subjunctive mood.
There are less than 70 optatives in the entire NT. In general, it can be said that the optative is the mood used when a speaker wishes to portray an action as possible. It usually addresses cognition, but may be used to appeal to the volition. Along with the subjunctive and imperative, the optative is one of the potential or oblique moods. (GGBB p. 480)
See the volitional moods.