One of the music theory things it took me a while to understand is why different major keys matter. In an idealized world, one can start a scale on any frequency and move up in whole and half steps (WWHWWWH) and have a scale. So why talk about the "key of G" vs the "key of C" if all that denotes is the frequency of the note we start on (which can be shifted up or down arbitrarily to suit the range of the instrument or vocalist)? The answer lies the physics of frequencies. The notes are not exactly the same from key to key because the whole and half steps are not exactly the same width. A perfect "fifth" (e.g., C & G played together) from a frequency perspective (meaning the two frequencies that resonate together creating a harmonic one octave above the lower) has a frequency ratio of 3/2 meaning the G is 1.5x the frequency of the C. The octave has a ratio of 2 (the high C is twice the frequency of the C below it). G is 7 half steps above C and the octave is 12 half steps. So if we walk our way up the piano in fifths, after 84 half steps, we would have a note (3/2)^12 = 129.75x the original frequency. But if we do the same on the octaves, we get 2^7 = 128x the original frequency, so the note we need to make all the major fifths sound right is different from the note we need to make the octaves sound right. The two are diverging slightly. So the result is that we can tune an instrument perfectly in one key only or we can tune it in a compromise of all the keys which sounds okay over a short range but sounds worse as we try to cover a wider range. If you're interested, there's lots of good reading on the subject (google "well-tempered" or "meantone").

EDIT: I realized I assumed a key concept in there. When two notes are played together, a third is heard (the "beat" frequency). If f1 and f2 are the frequencies of the notes being played, f2 - f1 = the beat freq. An octave sounds nice because the beat disappears (2f - f = f, so the beat is the same as the lower note of the octave). Other "pleasant" chord combinations are ones in which the beat does not clash with the first two note (e.g., is an octave of one of the notes).