A modem (in its traditional meaning) is a device which enables a
point-to-point data link to be carried over the analog
telephone system (PSTN, also called POTS, or Plain Old
Telephone System), thus:
Modems are sometimes said to "convert digital data into analog
form". This is highly simplistic. A better description would be
that a modem encodes data into a form which
maximises use of the telephone system to give the highest possible
bit rate.
The two modems involved in a connection
negotiate the highest common bit rate that each
modem, and the current phone line/link can support -- in current
models, up to 56kbps on the "downlink" side and 33.6kbps on the
"uplink".
Modems perform"on the fly" data compression (where possible)
giving higher "apparent" data rate.
They also perform (under some conditions) error detection and
correction -- for example, they are able to recover from some line
errors due to noise bursts, etc.
Traditionally, a modem interfaced to a computer using an RS232
serial link. Nowadays, internal modems are
commonly plugged into an expansion (eg PCI) slot. Whilst this is
considerably more convenient, debugging a misbehaving internal
modem is (in the author's experience) near
to impossible.