"For this alliance may so happy prove,
To turn your households' rancour to pure love."
Friar Laurence tells this to Romeo in Act 2, scene 3 just after he had agreed to secretly perform the marriage ceremony in his cell, confirming the two lovers' bond. His remark expresses his hope that the marriage would be received with joy by the houses of Capulet and Montague and thus bring to an end the age-old strife between the two families.
The friar acts as middleman throughout the affair. His kind-hearted meddling seeks to find a positive outcome for the two lovers and their feuding families. Friar Laurence's romantic belief is, however, naïve. In his desire to do good, he tends to ignore reality: that the rift between the families is very deep - it has existed for generations and many members and allies from both families have died because of their hatred for each other. A clandestine affair followed by an elopement is bound to lead to greater resentment and anger.
This misguided belief leads to further complications. Friar Laurence's plans do not quite work out the way he assumed they would. The friar had not prepared for other contingencies and had ingenuously believed that things would work out, but they do not.
The friar's desire for peace between the families is commendable, but ironically, it is his good-natured meddling which results in the final tragedy. His letter, informing Romeo of Juliet's fake death, does not reach its destination. Romeo goes to the burial chamber, finds Juliet dead and drinks poison, killing himself. Juliet awakens from her death-like slumber, finds Romeo dead beside her, and kills herself.
The greatest irony of all lies in the fact that the outcome of these tragic events is exactly the result Friar Laurence wished to achieve, for the families, that is. However, it is not "this alliance" which proves "happy" and turns the "households' rancour to pure love." It is, instead, the tragic and unnecessary deaths of the two best-loved members of the houses of Capulet and Montague which brings them together.
Lord Capulet rightly declares that Romeo and Juliet were:
"Poor sacrifices of our enmity!"
I've always believed that the Friar helps marry Romeo and Juliet becuase he sees their union as a chance to end the feud between the two families. If he can marry the two, and give the family time to accept it, he can help return peace to the streets of Verona.
This shows us that the Friar is a kind man, but is also a practical man. The feud has been going on for too long and has taken too many lives. The Prince has already decreed that if the two families spill any more blood there will be harsh punishments, so the Friar, who is responsible for the souls of all his parishoners, wants them to have peace.