Short answer: BGP MED, also called MULTI_EXIT_DISC, is an optional non-transitive BGP attribute used to suggest which entry point a neighboring autonomous system should use when it sends traffic into your AS. RFC 4271 defines it as a four-octet value that can help discriminate among multiple entry points to a neighboring AS, and Cisco and Juniper both document the operational rule most engineers remember: lower MED is preferred when MED is compared.[1][2][4]
The practical catch is important: MED is a hint, not a command. It can influence inbound traffic from a directly connected neighboring AS, but it does not override that neighbor's local policy, local preference, AS-path decisions, hot-potato routing, or provider-specific traffic-engineering rules.