Every Sunday from 6:00AM to 12:00PM (6 in the morning to noon), Joan the turnip seller will come to your town having two kinds of turnips to sell. The white turnips can be sold back to Tom Nook sometimes for a profit, just make sure to talk to him several times a day as the price Tom Nook offers for them can change many times during the same day. Be sure as well to sell them before the following sunday, as they will rot and won't be worth anything at all by then! Practice makes perfect, so just check the prices often and you might get lucky enough to have the turnips sell for over 600 bells each!
There's a couple tricks to white turnips. If you have the turnips left on a table in your house, it will never rot. To do this, drop an item in front of a table, stand on top of that item, then drop the turnips and it will be dropped onto your table. Also the turnips can be sold at your friends towns, so be sure to check turnip prices in their towns as well for big bucks! (or big Bells, rather)
Joan the turnip seller will also weekly have one bag of red turnip seeds available. After you plant the seeds, make sure to water the turnip daily to sell it at the end of the week for 16,000 bells to Tom Nook! Be aware however, if you miss just a single day watering it, it'll rot and won't be worth a single bell.