General term coined by Gateway to describe Amiga Models before the AmigaOne. The Classic systems, from the A2000 to the A4000T, can run AmigaOS 1.x to 3.x without expansion (the exception is the A1000 - this uses a Kickstart disk, which is not big enough to hold the newer ROMs). All "Classic" Amigas make use of the Custom Chipset.
Despite their age, Classic systems can be heavily upgraded (there were many years between the A4000T and the AmigaOne. Upgrades include:
An A4000 or possibly A1200 with these expansions should be capable of running AmigaOS4 and MorphOS. A really expanded Classic Amiga may only use the Custom Chipset from the original motherboard for legacy purposes - they are very useful as a bridge between AmigaOS3.x and AmigaOS4 or MorphOS.