Her mission is to kill Bill, a character whom little is revealed about until later in the film. The film is made in a typical mystery genre fashion revealing very little about the plot until the last twenty minutes of the second volume. Volume one and most of two, are simply comprised of Uma Thurman killing people and flashing back to her various trainings in martial arts.
A very cleverly made movie with great action sequences and original characters direct from the imagination of Tarantino. Great viewing overall.
If you like Kill Bill you might also like Battle Royale which also stars as one of it's characters Chiaki Kuriyama (Gogo Yubari from Kill Bill volume one).
To understand whats going on, you do have to be somewhat intelligent, but if your not, no biggie.
The action is awesome and the acting is amazing, everyone can appreciate the theatrical violence.