Time traveling is the act of changing the system's date and time on your computer in order to get rarer fishes faster.
It is recommended that you do not time travel, because once you time travel, you can't go back. This can cause your fish to be horribly depressed (if your fish are totally stoked, pumped, etc this will happen if you travel 7 or more days) and can cause the store on certain days to be temporarily unstocked.
Once you time travel, you can't go back, so think before you do this. If you travel to a date way far into the future, you would have to wait for the number of days you have traveled for the cycle to run again.