A Japanese sports expression meaning, literally, more losses (than wins, obviously).
In sumo getting makekoshi means that the sumotori has suffered losses in more than half of the bouts in a particular basho. This means 8 losses in a 15-day basho, and 4 losses in jungyo (7-day tournaments, held around Japan in even numbered months)1.
Makekoshi in a basho will affect the sumotori's ranking in banzuke - the ranking list. He will be demoted to some extent2, the smallest demotion possible being a step from East to West. This means a wrestler can go from being eg. maegashira 5 east, to being maegashira 5 west.
For ozeki and yokozuna different rules apply. Yokozuna cannot be demoted at all, but they are expected to withdraw if they begin to perform poorly. Ozeki can suffer makekoshi once with no demotion, but he must achieve kachikoshi (more wins than losses) in the following basho - or be demoted from ozeki rank.
- Results in jungyo does not affect the ranking in banzuke.
- At the very least makekoshi will mean that the sumotori does not get promoted.
My sources are Sumoforum.net and countless hours of watching sumo.