Each pitch generates a sound wave at a particular frequency. These are like the ripples in a pond if you throw a stone in, and like ripples have peaks and troughs. Concert A 440Hz is producing 440 ripples per second.
If you play two notes together which are exactly the same frequency, the peaks and troughs will match exactly so the sound is pure and in tune.
However if one note is 440Hz and the second is, say, 445Hz, the peaks and troughs won't quite match, and every so often the trough of one will meet the peak of the other and cancel it out. This is interference and produces an audible beat - think of the choppiness in the water that you see if different-sized ripples (from different stones) overlap.
If one note is exactly twice the frequency of the other (e.g. one is 440Hz, the other is 220Hz), the peaks and troughs will still be in step, so the sound is still pure and in tune; the notes are an octave apart.
A quick google threw up
this site on beats. The text may be a bit technical but the illustrations are quite good if they don't make you cross-eyed, and there is also a sound sample.
Sorry, that was more long-winded than I intended!