According to StormFax.com, as the Mayflower was passing just offshore from Cape Cod of what now is Massachusetts, when it encountered strong southerly winds and heavy seas in shallow water.
So the pilgrims decided it was too dangerous to continue south, so they turned back to the north to have the wind at their back. They eventually found calmer weather after rounding the tip of Cape Cod and continuing north. The winds eventually brought them to Plymouth two days later, and the rest is history.
You can read up on the entire story at www.stormfax.com/thanksgv.htm