The verb plaire is most often used in the expressions s'il vous plaît (formal) and s'il te plaît (informal), which, as you probably know, both mean "please"––or more accurately, "if it pleases you." "To please" is the basic meaning of plaire:
Ça peut pas leur plaire.
That can't please them.
Caption 18, Le Journal - Yann Arthus BertrandPlay Caption
Another way of saying "to please" is faire plaisir (literally, "to make pleasure"):
Je sais que ça va pas te faire plaisir
I know this isn't going to please youPlay Caption
If something pleases you, that means you like it. Indeed, plaire can also mean "to like" or "enjoy":
Une autre œuvre qui me plaît beaucoup
Another work that I like a lotPlay Caption
OK, je te plais pas.
OK, you don't like me.Play Caption
Ce livre plaît à tout le monde.
Everyone enjoys that book.
We could certainly translate the above examples as "another work that pleases/appeals to me a lot," "OK, I'm not pleasing/appealing to you," and "that book is pleasing/appealing to everyone." But plaire is used a bit more generally than "to please," so you'll usually see it translated as "to like" or "enjoy" with the subject and object inverted (ce livre plaît à tout le monde = everyone enjoys that book). Note that plaire always takes an indirect object (plaire à quelqu'un, "to please/be pleasing to someone").
When plaire is reflexive (se plaire, literally "to please oneself"), it means "to be happy" or "to enjoy being somewhere":
Est-ce que tu t'y plais?
Are you enjoying yourself here?
Caption 24, Yabla à Nancy - Université Nancy 2Play Caption
Elles se plaisent à Lindre
They like Lindre
Caption 21, Lionel - à Lindre-Basse - Part 6Play Caption
Or, in the plural, it can mean "to like one another," "to enjoy each other's company":
Ils se sont plu immédiatement.
They liked each other instantly.
And for life's unpleasant moments, there's the verb déplaire (to dislike, displease, irritate, upset):
Ses plaisanteries déplaisent à ma mère.
My mother doesn't like his jokes. (His jokes irritate my mother.)
There's also the expression n'en déplaise à (with all due respect to, with apologies to, no offense to):
Pas de fiole de cyanure, n'en déplaise à Shakespeare
No vial of cyanide, no offense to Shakespeare
Caption 47, Grand Corps Malade - Roméo kiffe JuliettePlay Caption
We hope you're pleased with this lesson on plaire!