In a semispace collector, the heap is divided into two equally-sized spaces, called 'semispaces'. One of these is defined as a 'fromspace', and the other a 'tospace'. The allocator allocates to the tospace until it is full.
When the tospace is full, a stop-the-world GC is triggered. The mutator is paused, and the definitions of the spaces are flipped (the 'tospace' becomes a 'fromspace', and vice versa). Then, the collector scans each object in what is now the fromspace. If a live object is found, a copy of it is made in the tospace. That is to say, live objects are copied from the fromspace to the tospace. After every object is scanned, the fromspace is cleared. The GC finishes, and the mutator is resumed.