Myrcella Baratheon is Joffrey's sister and is the second of the three children born of the incest between Jaime and Cersei Lannister (Joffrey, Myrcella and Tommen, in that order). Myrcella has Cersei's beauty, but is described as being a much brighter soul than her mother. Until now, she's pretty much been in the background of all that has occurred in King's Landing, leading to Joffrey's claim of the throne.
However, with her brother's claim being challenged left and right, Myrcella has suddenly become a useful piece in the game: through the right marriage arrangement, the Lannisters can conceivably build strategic alliances with other noble houses. It's just a question of who should get Myrcella's hand...
Bronn took the prudent step of helping out Tyrion Lannister in his hour of need. That loyalty rewarded the mercenary (called "sellswords" in GoT terms) the opportunity to greatly advance his position in life, thanks to Lannister gold in his hand.
Like any thirsty man who happens upon a well, Bronn knows to stick close to his diminutive new employer. But Tyrion will have many foes waiting for him in King's Landing, and as The Imp knows, the danger with sellswords is that they are only loyal to whomever is putting the most gold in their hand at the present time.