Radio Direction Finding (also called RDF) is a solution to a simple but common problem: if a radio transmitter is broadcasting, can you find its physical location using a receiver? The answer, of course, is yes. There are a bunch of reasons you might want to do this. The most common (and probably earliest) was for location and/or navigation. If you install fixed radio beacons at known points, you can use RDF to determine where you are relative to them, which will tell you where you are on a map. This is extremely handy, and forms the basis of every radio navigation system from LORAN to VORTAC to GPS.
Original RDF systems were radio receivers with signal strength indicators which had movable directional antennas. The operator of the system would tune to the desired beacon or transmitter, and then rotate the directional antenna through at least a full loop and note the bearing at which the antenna produced a null - this would be the direction where the antenna's 'hot' angle was at 90 degrees to the source of the signal. This would give you two possible directions for the source, and standard practice was to then move the RDF system a known relative distance and try again, then triangulate. Better antenna tech eventually allowed single-direction finding with a single antenna, so a rotation would give you a direction; in that case, a second reading would give you a relative location, as well.
There's another use for RDF, of course - that of trying to find the location of something that might not want to be found. As soon as radios went to war, there was someone trying to determine where broadcasts were coming from (usually so that they could do that location mischief). The military went to work making the process of RDF quicker and more reliable. As time and technology marched on, the systems got smaller, more accurate, and easier to use. The addition of a motor to the antenna and some simple analog circuitry allowed it to handle the rotation and signal-strength measuring by itself; this was called ADF (Automatic Direction Finding), and a press of a button would give you a bearing.
The signal sources used to navigate with RDF/ADF were (and still are) called Non-Directional Beacons, or NDB in modern aircraft/maritime navigation parlance. The beacons themselves do not transmit bearing data; they merely transmit recognition information which allows them to be identified, and perhaps their own position if they're especially helpful NDBs. Eventually, technology got even better, and directional beacons appeared which could helpfully tell you what bearing you were from the transmitter. This was still RDF, but with much of the task offloaded to the beacon itself. This technology eventually became LORAN and VOR.
Even these more modern equivalents, though, don't tell the navigator directly where he or she is. They'll just give you a bearing relative to the beacon. Some, like VOR/DME, will give both a bearing and a distance from the beacon, which (if you have a good map with you, of course) will tell you where you are if that map has the beacon's location on it.
Modern military communications places a great deal of importance on being difficult to jam or locate. Burst transmissions, spread spectrum radios, frequency-hopping - all these tricks and more are used to make it difficult to interrupt or locate communications. Against these, classic RDF doesn't work that well - but doing RDF from enough locations via dispersed sensors can still help.