The term Seabees comes from "CBs", which stands for "Construction Batallions". The day to day work for a Seabee varies depending on what their actual job is. When I was a young sailor, I spent a few months working with Seabees as we closed my base down. I was essentially apprenticed to the BU (builders) team at the time, but did work a bit with some of the other groups. The BUs seemed to function as the multi-purpose general contractors. We would do things like repair walls and ceilings, perform structural improvements in base housing, light demolition (tearing down walls or breaking up concrete). During my time there, I also got friendly with the CMs (construction mechanics), who maintained the base's motor pool vehicles, as well as all the construction equipment. Sometimes, when things were really broken, we had to rely on the SW (steelworker) to bring the welding equipment over and put things back together.
In short, the Seabees handle all the construction and public works type jobs. They build things and maintain them. They are a wonderful, fun, group of professionals. If you're interested in the trades, I highly recommend meeting with some Seabees and hearing more about it from them. Your local Navy Recruiter should be able to help you out with this.