All of the official legions (there were some units that called themselves legions, but weren't) were State-authorized combined-arms units, usually composed of a battalion of infantry, a battalion of cavalry, and a company or two of artillery.

A legion was sometimes organized, financed, and equipped, by a wealthy patron.

The C.S. War Department fairly quickly broke the legions down into separate components, the main reason being that military doctrine, command structure, and supporting arms capabilities at the time of the Civil War really had no place for a self-sustained combined-arms outfit.

As Len pointed out, the "legion" concept is one that 20th century soldiers will readily recognize, and most have served in; so it was a concept ahead of its time.