A pun is a word or phrase that has multiple meanings and is often used to create ambiguity about which meaning the writer intended. They are used for humor. The phrases "pun intended" or "pun not intended" refer to this.
Here are some from Act I Scene IV, the pun is in bold:
ROMEO Give me a torch: I am not for this ambling;
Being but heavy, I will bear the light.
[Light is a pun. Romeo is feeling "heavy" meaning sad/upset. So light here not only refers to the light of the torch but also the lack of lightness in Romeo's mood.]
MERCUTIO Nay, gentle Romeo, we must have you dance.
ROMEO Not I, believe me: you have dancing shoes
With nimble soles: I have a soul of lead
So stakes me to the ground I cannot move.
[sole and soul are spelled differently but pronounced the same, they are puns]
ROMEO I dream'd a dream to-night.
MERCUTIO And so did I.
ROMEO Well, what was yours?
MERCUTIO That dreamers often lie.
ROMEO In bed asleep, while they do dream things true.
[dreamers lie, as in, do not tell the truth]
ROMEO Is love a tender thing? it is too rough,
Too rude, too boisterous, and it pricks like thorn.
MERCUTIO If love be rough with you, be rough with love;
Prick love for pricking, and you beat love down.
[the other meaning of prick here is "urge," most probably in this context, it refers to sexual urges. Mercutio may be suggesting that Romeo overcome his heartbreak and pain by becoming intimate with another woman]
Here are a few:
"Mercutio: If love be rough with you, be rough with love.
Prick love for pricking, and you beat love down."
"Romeo: I dreamed a dream tonight.
Mercutio: That dreamers often lie."
"Mercutio: Being but heavy, I will bear the light."
"Mercutio: You are a lover, borrow Cupid's wings / And soar with them above a common bound."
Sorry I don't remember the lines or anything, but hope this helped!