Soundcheck is just that - a check of the sound. During soundcheck, the musicians set up their instruments, plug in and try out a few songs. They work with the sound engineer to get the right levels for everything - both the mix that the audience is hearing and what the musicians are hearing on stage. The sound engineer keeps track of everything, and then when the musicians take the stage in front of the audience, the sound should be just right (in theory, anyway!).
Soundcheck usually happens about an hour or so after load in. The headlining act gets to soundcheck first, partly because it's a privilege of being the headliners (when you soundcheck first, you usually have a nice, long break before you have to play) and partly for logistical reasons. If the opening band soundchecks last, their gear can be left on stage all set up so that they can just walk out and play when it's time for the gig to start.