High brass shells are shotgun shells that have a brass base (or head) that extends up the body by about 3/4" or so. Low brass hulls extend up the body by 1/8-1/4" or so. In paper hulls (now rarely seen) high brass is used for reliability of extraction. High brass was used in the early plastic hulls to prevent splitting and burn thru; it is mostly no longer needed due to improved plastics. In modern shot shells, the only real difference between high brass and low brass hulls is a marketing difference. Powerfull factory loads use high brass hulls, while standard or target loads use the low brass hulls. There is no correlation between the mechanical strength of the hull and amount of brass in the base.
ACTIV hulls don't have a brass base, they are entirely plastic except for a metal button in the case head that holds the primer and forms the rim.
Most shotgun shells can be had in a variety of lengths; typical lengths for 12 gauge shells are 2-3/4", 3" and 3-1/2". These lengths refer to the fired length of the hull, not the loaded length. There can be significant difference in the power level of different hull lengths in the same gauge. The extra length allows more power and shot be put in the same case. NOTE: It is _very_ important that you use the shell length that you shotgun was designed for or shorter, but nothing longer! If your shotgun is marked 2-3/4" 12 gauge, do _not_ put 3" shells in the gun. However, for instance, if you have a 3-1/2" 12 gauge, you can (generally) use the shorter shells in that shotgun.
Of course, never mix gauges, a 20 gauge shell will fall into the chamber of a 12 gauge untill the rim is caught by the forcing cone. Then when you notice your chamber empty, and load a 12 gauge shell on top of it and fire it, your gun blows up.