Boarding is when members take care of another member's wolf for a variety of reasons: out-of-town, expectant females, need space, want some wolf training done, etc.
You "sell" the wolf to another user for 0 mushrooms (or for extra security, apples), they take it they take care of it for the agreed time. You pay them, then you take the wolf back from them once the time is up.
Take caution, because there is a large risk involved. A lot of players like to poach low-cost wolves and free-range them, sometimes for quests, sometimes because they're really bored. I'm guilty of doing this myself (although I haven't done it as often as I used to). Sometimes, people don't pay attention when a wolf says "Reserved".
Do realize that boarding and wolf transferring between basic members is not supported by moderators. Whatever wolf gets put up for public sale goes to whoever buys it. Whoever bought the wolf can do what they want with the wolf.
Winter Month: 2 
Night 
Blizzard Moon: 
