Sources: Wikipedia, Weather.US and Boldmethod

A dry line (also called a dew point line, or Marfa front, after Marfa, Texas) is a line across a continent that separates moist air and dry air. A dryline is defined simply as a boundary between airmasses that have similar temperatures, but different moisture levels. Unlike a cold or warm front, one airmass is not rapidly overtaking the other. Additionally, the temperature on either side of a dry line will be similar, meaning there isn't a large temperature gradient.

The dry dense air acts like a wedge, lifting the less dense moist air. This behavior creates lifting action, but it is typically weaker than a cold front. However, with enough wind shear aloft, significant lifting action can occur, forming severe weather. One of the most prominent examples of such a separation occurs in central North America, especially Texas, Oklahoma, and Kansas, where the moist air from the Gulf of Mexico meets dry air from the desert south-western states.

The dry line is an important factor in severe weather frequency in the Great Plains of North America. In the dry sector west of the dry line, clear skies are the rule due to the dryness of the air mass sweeping in from the Desert Southwest. Cumulus clouds are common east of the dry line in the moist sector, though they are taller with greater development along the dry line itself.

Here’s a visible satellite image from before convective initiation (the time the first thunderstorm develops). The dryline is clearly visible as the boundary between air that's too dry to support any clouds and an area that has enough moisture for a bunch of clouds.

You can identify a dry line by looking at a graphical depiction of the dewpoint. You can expect a dry line to have cumuliform-type clouds with extensive vertical development on the east side. On the west side you might see clear skies, or with an unusually strong dry line, you might see dust storms that are caught in the dry line's updrafts.