Pickup soccer is an informal version of soccer, where participants meet at a field with little restriction i.e. you can come and go as you please. The field often times does not have goals and/or there aren't enough people to play with goalies. In this case, goals are made with two arbitrary objects each, usually two shoes or two backpacks, and goals are only counted when the ball rolls through the two "posts" i.e. it must stay on the ground.
The point of pickup soccer is to get some exercise, to play soccer, and most importantly, to have fun. Individuals who desire competition often do not participate, as they do not find the experience enjoyable. There are usually no restrictions on skill level, sex, age, or race, so long as one is fit enough to play and respects others' abilities.
Apparently Davis, CA doesn't have any advertised pickup soccer groups. Please post a comment if you have an interest in forming such a group.