When you are connected to your hosted computer you are running your programs on the the hosted computer not on the device (PC, tablet, etc.) you are connecting with.
This means that if you try and save something to “My Documents” it will be saved on the hosted computer by default. The hosted computer can see all the drives on the device you are using to connect but has to rename them to differentiate them from its own drives.
By default the "c:" drive on your device will appear in the list as "m: (Client_c)"
So, saving files to the "m:" drive will save them to your local device
The "m:" is also used to read files from your device