I'm not entirely sure what scene you are specifically referring to, but I can hazard a guess. The first time that Romeo meets with Friar Laurence is in Act 2 Scene 3.
It's clear that Romeo and Friar Laurence are close, because Friar Laurence can tell simply by looking at Romeo that he is tired and didn't sleep. Romeo admits that he didn't sleep, and Laurence immediately asks "Wast thou with Rosaline?" That's a huge indicator that the two of them are close. Friar Laurence knows Romeo well enough to know who Romeo has been infatuated with lately AND ask him if he was having sex with her.
Another indicator that Romeo is close to Friar Laurence and trusts him is that Romeo immediately tells the Friar that he is in love with Juliet and wants to marry her. You don't announce to a casual acquaintance that you crashed the household of your sworn enemy and have fallen in love with his daughter.
Further evidence of their closeness is Friar Laurence's willingness to give Romeo a hard time about Rosaline.
"Oh, she knew well
Thy love did read by rote, that could not spell."
Basically Friar Laurence shares that he knows how Romeo attempted to woo Rosaline. Romeo used a bunch of cliche, cheesy love lines on Rosaline and she knew it. Again, Friar Laurence would not know this kind of info unless he and Romeo are close and talk frequently.