Like with all crops, more and more turnips will slowly spawn on gameworlds where players are active.
Turnips can be consumed raw and will then provide 100 additional maximum Health Points for a few minutes, but it will not heal player characters. So this is not an efficient way to use Turnips.
Then these Seeds can be planted on tilled land (use the Plow on Grass or Dirt) in appropriate Biomes with some Water nearby, so more turnips can grow. Read the article Farming to learn more about how to grow crops.
Turnips can be used to cook Turnip Sandwiches, many different Pies or Soups in the Cooking Station. The Cooking Station only provides 4 cooking recipes, but by choosing different ingrediences, you can cook up to 36 types of Food with different positive effects (buffs) when consumed (either right click on the Food after putting it into a quickbar, or drag a stack of Food from the inventory over your character's portrait on the right side).