A overglorified SoundCard masquerading as a MoDem. The hardware consists of little else than a DAC/ADC, whereas the actual signal processing logic is performed by the host computer's CPU. The software masquerades as a "driver", which is generally available from vendors only for MicrosoftWindows.
Intel now has a supported WinModem chipset (DSE sells MoDems based on these) and because they have both MicrosoftWindows and Linux drivers Intel calls them HaM, "Host-accelerated Modem". How a 56K WinModem is "accelerated" in comparison to a 56k hardware modem isn't entirely clear; this appears to be MarkeTroid speak.
By far the most common WinModems (at least in NewZealand) are ones based on Conexant chipsets. For a long time there was no way at all to get any of these to work in Linux, but at some point they released Linux drivers.
If you want to get a new MoDem for a Linux and would like to avoid the cost of a hardware MoDem, DanielLawson recommends a Lucent or Agere compatible chipset based WinModem, after good experience with a Lectron I56LVP/F4 ($32 as of May 2004) that runs fine with the ltmodem drivers. If the binary Package doesn't work for you, get the source package and follow the instructions, there's a couple of scripts you can run which basically automate the whole installation.
Some modern distros include drivers for the more common WinModems.