To put this quote into context, Tybalt has just insulted Romeo by calling him a "villain." He has also challenged Romoe to draw his sword and have a fight. In response, Romeo refuses to accept this insult because he says he has never done anything harmful to Tybalt ("never injured thee").

In addition, Romeo goes on to say that he loves Tybalt more than he could ever know. He also says that he loves the Capulet name more than Tybalt realizes. This is significant because Romeo is alluding to his secret marriage to Juliet. By marrying her, Romeo has become part of the Capulet family and, therefore, no longer feels any hatred for Tybalt and other members of Juliet's family.

As a result, Romeo urges Tybalt to "be satisified." In other words, he wants him to calm down and back off and to accept his declaration of peace because it is genuine.

Of course, Tybalt has no idea that Romeo has married Juliet, so he will not back down. Tybalt's refusal to back down, however, is an action that will soon cost him his life. 

What is going on here is that Romeo is trying to calm Tybalt down.  Tybalt wants to fight him but he does not want to fight Tybalt.  This is because he is now married to Juliet and so he sees Tybalt as a relative.

What he is saying here is essentially this:

I'm telling you, I never did anything bad to you.

I love you more than you will understand until you find out why I love you.  So, Mr. Capulet (I love that name as much as my own), do not be angry.