"Backdoor" buying and selling refers to an arrangement between a supplier and a customer that circumvents the customer's normal purchasing rules. Metaphorically speaking, the supplier is dealing with the company through the "back door" rather than at the front of the shop, where legitimate business gets done. Backdoor deals are problematic from an ethical standpoint, and in some cases may even be illegal.
Backdoor buying is most common in situations where organizations are supposed to obtain bids from multiple potential suppliers before making a deal. A supplier might get in through the back door by building a relationship with executives in the organization, who would then direct their purchasing agents to order from that supplier. Or a supplier could offer kickbacks to a purchasing agent, paying him under the table to choose that supplier. When there's a backdoor arrangement in place, the company might still field bids from other suppliers, but since the ultimate purchasing decision has already been made, it's doing so only for appearances' sake.
Organizations don't put purchasing rules in place just to complicate things. They want to get the most value for their money, and things like competitive-bidding requirements are designed to make that more likely. People within the organization who cut backdoor deals may well be damaging their company's competitive position. In situations where purchasing rules are actually legal requirements, as is often the case with government agencies, backdoor deals can be illegal.