It's by no means definitive, but this link states that it's because, when overarm bowling was introduced, another fielder (to complement slip and point) was needed - this was the third fielder, hence third man.
This link, however, gives a subtly different interpretation.
The first link also gives these explanations:
Gully - Refers to the gap or 'gully' that exists between the slips and point
Cover - Refers to the position that 'covers' the point and middle of the wicket
Mid off and mid on - Shortenings of the terms 'middle wicket off' and 'middle wicket on'
Silly Mid On - the mid on is self explanatory, however it is believed that the silly refers to an old definition of silly, meaning ...