Coltrane actually wrote this tune when he was trying to get a good handle on "Have you Met Miss Jones?". I forget who originally asked John "why did you write Giant Steps?" but my sax teacher, Bob Mover has a million stories like this and he said that Trane did it to get a better handle on Miss Jones. After playing both tunes and not having a good handle on either one, I'd have to say that if you can play Giant Steps, you can play Miss Jones...
The reason Trane did this is because the bridge of Miss Jones is a series of II-V-I progressions in descending major thirds. Well, the last major third is not descending, but it's still a major third (up). The bridge looks like this, essentially:
BbMaj -> GbMaj -> DMaj -> GbMaj
Of course, the above pattern is a series of II-V-I's but the key centres are the ones given. You can see that they are just keys that are a major third apart, and that is what Giant Steps is, as Footprints states quite clearly.