"Te metiste" means "you got into", as getting into trouble, or getting into some place. As a slang it could also mean that you inserted something into your body (food, drink, drugs...). Figuratively it could also mean many different things:
Te metiste en problemas → You got into trouble
Te metiste en el bar → You entered the bar
Te metiste un filete → You ate a steak
In this particular case, "Te metiste" means "You entered":
Te metiste completamente en mi vida → "You entered completely in my life". Notice that in other contexts, "meterse en la vida de alguien" would mean "to meddle in the life of someone"
The name Plebes del Rancho means, in mexican (because it's a mexican band, in other countries it would have a slightly different meaning), Ranch boys, with "plebe" meaning that, boy, or cubbish/disrepectful boy. Its root is the same as "plebs".