"Active" cables have active circuitry in them--in the original (Schoeps), a low-noise field effect transistor (FET) and associated parts are in the head (capsule) end of the cable, so that the signal in the cable is run at low impedance. This makes the arrangement far less susceptible to interference and losses than in the older type of passive capsule extensions which could never be more than a foot or two long before stray capacitance and RFI became a problem.
Since the original active cable arrangement was patented in the mid-1970s, during the lifetime of that patent all the other manufacturers had to come up with distinctly different arrangements. For example, Neumann's capsule extensions aren't "active"--their capsules are. But most people here don't seem to care about the difference since the effect is more or less the same--either way, you can separate the capsule from the amplifier and use a cable in between.
--best regards