Lets say your whole tilemap is 256x256. Creating the whole tilemap as one mesh would be very impractical and even if possible in Unity (it isn't, due to the 16bit index limit), it would be incredibly slow to render. What the partitionSize does is it splits the tilemap into smaller mesh chunks. So, a partition size of 32x32, will split up the tilemap into (256/32 = 8)x8 chunks. The 8x8 chunks will get rendered a lot more efficiently, as each chunk is about the right size for the GPU, and doesn't have ridiculous amounts of polygons in it.
So thats it really. It partitions the "world" into AxB sized chunks. In most cases, you shouldn't have to care about it.