API stands for Academic Performance Index.
It is important because it ranks the state's schools. It is a way for parents and others to compare schools in the entire state. They can look at a school and say the children in that school (for whatever reason) do better, or worse on the State STAR Tests. The improvement in the API score represents better scores from the students.
My school site's API score improved by +39 points!! We still, though, have a long way to go...
We "rank" 6 out of 10 (the highest being a 10) in the State of CA. However, when looking at similar schools (which is a group of 100 schools that supposedly have similar demographics) we are a 5 out of 10.