Good question - and quite a difficult one to answer. Friar Laurence is a monk, with whom Romeo has struck up a very close friendship. He has odd beliefs (certainly unusual for a Christian friar!) and an unusual faith in nature and natural medicine:
O, mickle is the powerful grace that lies
In plants, herbs, stones, and their true qualities;
For naught so vile that on the earth doth live
But to the earth some special good doth give...
He agrees on the spot to marry Romeo and Juliet, in the hope that he can heal the alliance between their households:
For this alliance may so happy prove
To turn your households’ rancour to pure love.
He also provides sage counsel to Romeo about taking things slowly:
Wisely and slow, they stumble that run fast.
He alone among the adults in Verona seems to have the trust of both Romeo (who comes to him immediately after killing Tybalt, rather than return to the Montague house) and Juliet (who comes to him when she hears she has to marry Paris).
Yet Shakespeare provides a strange, discordant ending to his story. Though he's helped the lovers all the way through, he deserts Juliet at the last minute, in pure cowardice:
Stay not to question, for the watch is coming.
Come, go, good Juliet. I dare no longer stay.
The prince leaves it open at the end of the play as to whether the friar will be punished or absolved, commenting only that they had thought him "a holy man". However - in Shakespeare's source, the friar was hanged.
Friar Laurence is Franciscan monk who is able to conduct religious ceremonies such as weddings and burials; he is also able to listen to confessions and forgive sins.
Friar Laurence's personality is a bit of a paradox: he is a trustworthy person who does not always "play by the rules." For example, Romeo and Juliet are able to completley trust him with their "secret" love for one another. In fact, it is the friar who secretly marries the two. Obviously from Romeo and Juliet's, point of view, he is quite trustworthy and dependable. However, if you look at it from the other members of the communities point of view, such as that of the the young lovers' parents, Friar Laurence appears to be secretive and somewhat dishonest.
It should be noted, however, that Friar Laurence's actions are not dictated by his own selfish desires. In marrying Romeo and Juliet, he is thinking about the greater good of the community and of the happiness of the young couple. (Note: One of the major reasons that he agrees to marry Romeo and Juliet is because he hopes that it will reunite the Capulets and the Montagues.) Cleary, Friar Laurence is also a very unselfish and caring person.