The tag is a number attached to a sector, a linedef or a thing. A thing's tag is generally called a TID. The tag is used to refer to the tagged sector, linedef or thing through various action specials and built-in ACS functions. Several objects may share the same tag, and will be affected by the same effects.
UDMF maps have the ability to have multiple tags per line or sector. Doom and Hexen map formats do not allow this. Things cannot have multiple TIDs regardless of map format.