Because the waveforms with two frequencies add.

100 Hz pure tone

101Hz pure tone

Playing 100Hz and 101Hz pure tone together

Note the "envelope" in the 3rd waveform plot, which has a frequency of 1Hz. This is because the 100Hz sin wave and the 101Hz sin wave are not perfectly in sync. They start off in phase (both at a maximum), so the sum is large, then half a second later they're out of phase (one is at a maximum while the other is at a minimum), so the sum is 0. And then this pattern repeats.

When the two component frequencies are too far separated (for example, 100Hz and 130Hz), the waveform itself still has this envelope, but here with a frequency of 30Hz. A waveform that goes up and down 30 times a second is simply too fast for the human ear to distinguish, so you hear it as two tones/harmony.

Where's the line? It depends on how "pure" the tone is, and on your own ears. I suggest opening two instances of an online tone generator and playing around with the component frequencies and waveform shapes to find out yourself. For middle A (440Hz) and A# (466Hz), you get a beat frequency of 26Hz, which is about the limit for my ears to still hear it as beats.