We understand that the bass clef is called the F clef, while the treble is called the G clef. It's to do with where the strange signs are on each staff. But why those notes in particular?
I don't really know the history enough to be certain, but I imagine it comes out of the Medieval hexachord system where the three hexachord types were based on
Like Michael says the C- and F-clef come from the Guidonian hand ans show where the semitone lies: below C or F
When F was altered to the lead tone F# the semitone was lying below G.
If we look at the 5 lines of the staff we couldn't see the semitones (without the clefs) as all lines have the same distance.
Riemann writes in his CATECHISM OF MUSICAL HISTORY
To these two oldest clefs, the g-clef, which showed once marked g, was already added in the 13th century; but for the music of that time, which was written exclusively for the voice, it was extremely seldom required. It was only in theoretical synopses, or at most in the sketching of scores, that V was written for our great G. As the clef originally showed the place where the semitonium lay, the g-clef at once indicated that f was raised to f$; therefore, where this transposition of keys into the dominant (which seldom happened), was not intended, and the g-clef was only chosen to avoid ledger lines, we often find a flat on the f line, as a sign that the lower form of f (fb molle, i. e. not f$, but f) is meant.