Tape Echo and Heads
The three heads in a "three-head" tape deck are erase, record and play. That's the order they appear in in the tape path (well, you'd pretty much have to put the erase head first, wouldn't you?).
Most current cassette decks and some reel to reels have only two heads. There's an erase head (you really need one of those), and a dual-function record/play head. In the old days (say '70s and earlier), tape decks generally had three heads, because they hadn't got around to engineering a head that could record and also playback well. In order to record well, the heads had to have a gap that was too wide to get good high-frequency response on playback (a playback head "loses" waves that are smaller than its headgap, which makes sense if you think about it).
Eventually, the engineers got this worked out, so one head can record and also play well. This is good, because it made the sort of overdubs we now take for granted possible (you can't overdub in sync if the playback head you're listening to is in a different place on the tape from the head that's recording). Even though they didn't really need a third head, manufacturers kept putting the third head on most of their machines, partly for old-times' sake, partly because buyers figured three heads must be better than two, and partly to facilitate bias adjustments. Okay, maybe entirely to facilitate bias adjustments ... I don't know.
The machine in your link is mysterious to me, though someone with more expertise on old reel machines might know something about it. If I understand the minimal specs under it, it looks like it's a two-track mono* machine that runs only at 3 3/4 ips. This suggests that it was perhaps intended for speech, rather than music. The standard "consumer" format for music, at least from the late '60s or so, was 7 1/2 ips quarter-track stereo, with some releases in "long playing" 3 3/4. Although the machine looks pretty old, maybe it has only two heads because high frequency response wasn't considered sufficiently important for its intended use.
*I.e. it records in mono on half the tape, then you turn it over and it records on the other half in the other direction ... pretty similar to quarter-track stereo (or a cassette tape), but mono.