Why were AA units (or ABA, ABBA, etc) usually run back to back?

A drawbar is a solid bar that replaces the couplers between two semi-permanantly attached units. As others have mentioned, they were used in TR units, between the controlling switcher and the booster (or B-unit).

You can see them now in 3-unit 53’ stacker sets (not the articulated units, but 3-unit sets). You can also see drawbars on triple-53 TOFC units, where a pair of TOFC cars carry 3 53’ trailers, with one straddling the two cars.