STA (Single Threaded Apartment) is basically the concept that only one thread will interact with your code at a time. Calls into your apartment are marshaled via windows messages (using a non-visible) window. This allows calls to be queued and wait for operations to complete.

MTA (Multi Threaded Apartment) is where many threads can all operate at the same time and the onus is on you as the developer to handle the thread security.