hence the Cross of St. George in the club badge
The St. George's cross is there because Sant Jordi (Catalan way of saying St. George) is the patron saint of Catalunya.
The red and yellow stripes on the top right of the badge are are taken from the flag of Barcelona (the city), which is a variation on the senyera, the flag of Catalunya.
How about the red and blue stripes on the bottom?
Those are their club colours.