An early bid is a way to cash in on players you have for sale, before their deadline ends. You list your player for 0€ or sufficient* below the expected selling price. Then you ask friends or fellow federation members to place a bid. This bid is expected to by raised by other users to normal marketvalue before the deadline ends, but the idea is to be able to spend the money you'll get for that player in advance, for instance to buy his replacement for an upcoming match.
* To be sure not to actually buy the player, sufficient is mostly considered to be max 75% of the expected price.