Definition: Multi-lateral peering is peering negotiated and established between potentially many parties via a shared route server.
A Multi-Lateral Peering Agreement (MLPA) is signed at exchange points that support multi-lateral peering. There is some initial configuration for this first session with the route server, but after that, you automatically hear the additional routing announcements as more companies peer with the route server. Some companies prefer multi-lateral peering since it minimizes the incremental cost of peering; peer with the route server and you hear the routes that the route server hears. Others prefer the direct control of bi-lateral peering.
Interestingly, there is a Mandatory MLPA required at the Hong Kong Internet Exchange (HKIX) and at the NIXI in India. Some ISPs meet the explicit requirement to peer with the route server, but resist the nature of the mandatory MLPA by announcing only a small subset of their routes.