OK, I'll give it a shot....
The audio signal is sent to the recording head via a head amp which superimposes a high frequency/high energy "bias" signal on the audio. The head turns the resulting waveform into magnetic impulses which cause the magnetic particles on the tape to have their poles arranged in an orderly fashion, the order being analogous to the signal being recorded. ("Blank" tape has random orientation of its magnetic domains.) On playback, the same magnetic particles passing by the playback head induce a current in the head which is fed into the playback electronics, which filter out the bias frequency and pass the audio signal on for further amplification.
Why do you need really good converters to come close to analog? One reason that comes to mind is that poor converters tend to have high jitter and low-quality filters, which leads to unpleasant distortion of the signal. Because of the high demand driven by consumer playback electronics, a high-quality D/A converter is less expensive than a high-quality A/D converter. That's why cheap onboard computer sound systems tend to play back great (or at least OK), but record very poorly.
Don
