It means that Avast probably detected that it's using a suspiciously big amount of memory at the time and created a dump itself (there's a "watchdog" for that).
Those dump files could tell us what was going on when the big memory allocation was happening and point us to the actual cause (though that assumes that the dump was created in the middle of the operation... if there was a leak, for example, meaning some memory is allocated and then forgotten - and left forever - the dump could be created later and the problematic action long gone. But if you say the memory goes back to normal after the scan, chances are it's not a leak but rather a operation that the dump recorded).
Of course, we would need to see at least one of those dumps to say more. I would say the dump files should be well compressible - if you compress it using 7-Zip (or even ZIP), I think it would go down a several hundreds of megabytes.
