The land bridge theory is that the Bering Strait is pretty shallow. During the Ice Age when a significantly greater percentage of the earth's water was locked up as ice in glaciers, sea levels were correspondingly lower. This allowed people to migrate across.

There is another competing (or possibly complementary) hypothesis for which evidence is mounting that many of North America's earliest inhabitants didn't arrive from Asia on foot, but rather on boats migrating along the coasts.

https://en.wikipedia.org/wiki/Settlement_of_the_Americas#Pacific_coastal_route

Not to detract from either of the comments above, there is a solid discussion by /u/RioAbajo in the FAQs on this subject. Skim down to about mid-way to the stuff about Beringia. The follow up comments also are worth reading.