The motherboard is the working part of a computer, together with the processor that's mounted on it. Everything else is effectively an 'add-on', including the hard drive that contains the operating system (Windows) and your data (such as your documents, pictures and iTunes library).
If the very worst happens, and the technician says that your computer is beyond economic repair (through a motherboard fault) all that he'll have to do will be to remove the hard drive (which takes a minute or two at the most), connect it up to another computer (dead easy) and 'take ownership' of it (a few quick key clicks).
The other computer (which might, for example, be the new one that he's just sold you) will then be able to access the data on the old hard drive in exactly the same way as if you'd plugged a USB memory stick into it. (i.e. the data could be copied to wherever you want, including onto the hard drive of the new computer).