Short for "RegionalExpress 160"; the product name for Deutsche Bahn's (DB Regio's, to be exact) fastest midrange trains.
As 160 km/h is the highest speed that can be reached on conventional German railway lines without LZB, the idea to make regional (non-InterCity) trains actually reach this speed instead of the more common 100, 120 or 140 km/h top speeds seems logical. An RE160 consists of air-conditioned or otherwise pressure-proofed double-decker carriages pulled by a loco that can do 160 km/h; while this might be some object of industrial heritage like a 111 or a 143, what the marketing guys like to have in front of an RE160 is a fashionable "RegioLok", the 146.
"RE160" has also become a popular designation for DB Regio's newfangled 160-capable double-deckers, even if they aren't doing RE160 service.