How are Romeo and Juliet's families alike, and why might this be important?

In the Prologue, the Chorus tells us that Romeo and Juliet is a play about domestic conflict. "Two households" (that would be the Montagues and the Capulets), "both alike in dignity" (of the same social standing) are going to be involved in a rather messy, and uncivil family feud.

Both families are wealthy and powerful in Verona. It's important because it shows the limits of power--even though they are rich and powerful, neither is able to save their child and both are victims of hate and vengeance. Also, it shows that fate triumphs over worldly power (the "star-crossed" lovers are fates to die--nothing can change that).