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A regiment is a title used by some military units. The size of a regiment varies markedly, depending on the country and the arm of service.
Historically, in the seventeenth and eighteenth centuries, a full-strength regiment was typically supposed to be a thousand men, and was commanded by a colonel.
Today, there is no set size for a unit calling itself a "regiment", which may be:
Less than a battalion-equivalent, e.g. Regiment of Life Guards
A battalion-equivalent, e.g. 3rd Foreign Infantry Regiment
A number of battalions (or equivalents, such as US squadrons) e.g. Royal Regiment of Scotland, 2nd Infantry Regiment (United States)
An entire arm of service; In several commonwealth countries, the entire artillery arm is often titled "regiment" (e.g. the Regiment of Artillery), and may then be sub-divided into "field regiments".