A "Winmodem" is a modem with the DSP removed and all the data compression and such done on the CPU. The "modem" itself is basically a glorified sound card. The chief disadvantage is that it slows down the CPU (and if your CPU is really loaded, can interfere with communications). Even worse, "Winmodems" cost a lot less to make, but are usually priced only a bit less than their fully-functional cousins. The modem makers love the increase in their profit margin.
There are a few ways to tell if you have a Winmodem. If your modem does not work in DOS, or has minimum system requirements ("Requires a Pentium"), it's probably a Winmodem. Even if you don't run Linux, it's probably a good idea to replace such a braindead modem anyway.
The other disadvantage is that the makers of Winmodems tend not to be willing to reveal the programming interfaces for their products. This means that Linux drivers would have to be reverse-engineered, and so far no one's been interested enough to spend the time for a modem that isn't worth much to begin with.
Winprinters are similar - they scrimp on printer power and memory and force the CPU to take up the slack.
Note that it is possible for Linux to use a Winmodem or print to a Winprinter if it is networked to a Windows box that has one. The Windows-modem-sharing mini-HOWTO describes how a Windows box can make its modem available for a Linux box to dial through. The Samba program allows Linux to serve and use Windows services, including shared printers.