The word describing the garment Peter put on is ἐπενδύτης, which is a hapax legomenon in the New Testament and rarely used in ancient Greek literature. Etymologically the word derives from a verb that means "to put on over". It is a garment (perhaps specific to the profession of fishing) worn over something else. So it might be better to think of Peter fishing in his underwear.
It is odd, however that Peter would add clothing before jumping into the water to swim 100 yards or so. (Peter's personality was such that it does not seem odd that he was so eager to get to Jesus that he wouldn't wait for the boat to get there.) W. Hall Harris III writes:
R. Brown’s suggestion seems much more probable here: the verb used, διαζώννυμι, does not necessarily mean putting clothing on, but rather tying the clothing around oneself (the same verb is used in 13:4-5 of Jesus tying the towel around himself). The statement that Peter was naked (ἦν γὰρ γυμνός) could just as well mean that he was naked underneath the outer garment (τὸν ἐπενδύτην), and thus could not take it off before jumping into the water. But he did pause to tuck it up and tie it with the girdle before jumping in, to allow himself more freedom of movement. Thus the clause that states Peter was naked is explanatory (note the use of γάρ), explaining why Peter girded up his outer garment (τὸν ἐπενδύτην) rather than taking it off: he had nothing on underneath.
In any case, it seems Peter was properly attired for his labor, but needed to prepare himself before jumping into the water. Either he needed to secure his ἐπενδύτην so that he could swim or he felt he needed to put on the garment in order to meet his Lord.