The meaning is different in UK and US English. In the US, it means "Completely sure." In the UK it means fairly (bastante) sure (as Alex explained).

Btw, in spoken US English, a very common way of saying bastante seguro would be "pretty sure."

Thanks! :D

Exactly! That's right!

Thank you Alex, so if I want to say: I am sure (100%) it would be: I am completely sure, right?

"Quite sure" it'slike: "I'm really sure". Which is more than "enough" but not 100% sure. Let's say, a 80% of certainty : )