Why did Romeo kill Tybalt in Act 3? Is it because of Romeo's character?How does Tybalt's death change the action of the play.

Concerning Shakespeare's Romeo and Juliet, in short, Romeo kills Tybalt because Tybalt kills Mercutio.  Of course, it isn't really that simple.

Romeo, newly in love with Juliet--a member of the hated enemy, the family that Romeo's family constantly feuds with--wants now to make peace.  While doing so, he gets in the way of Mercutio and Tybalt while they are fighting.  The two are partly serious and partly playing around, but the game is dangerous, since the game is sword fighting. 

In getting between the two fighters, Romeo inadvertantly causes Mercutio not to be able to react to a thrust by Tybalt, and the thrust mortally wounds Mercutio. 

Romeo becomes angry and loses control and kills Tybalt out of revenge.  At the same time, Romeo is probably lashing out at Tybalt due to his own guilt for having contributed to Mercutio's death.