The tabernacle is a liturgical furnishing used to house the Eucharist outside of Mass. This provides a location where the Eucharist can be kept for the adoration of the faithful and for later use (e.g., distribution to the sick).
It also helps prevent the profanation of the Eucharist. Thus the law requires, "The tabernacle in which the Eucharist is regularly reserved is to be immovable, made of solid or opaque material, and locked so that the danger of profanation may be entirely avoided" (CIC 938 §3).
The word tabernacle means "dwelling place." Any place someone dwells is a tabernacle. The term is also sometimes used for a temporary dwelling place. Thus the tent-like sanctuary that the Jews used before the Temple was built was called the Tabernacle, because God dwelt there. Similarly, for the feast of Sukkot the Hebrews erected temporary shelters to live in for the festival, which is often called "the feast of tabernacles" or "the feast of booths" as a result.
The tabernacle in Church is so named because it is a place where Christ dwells in the Eucharist.