The width of spectral lines is pretty much what the name implies. It refers to how wide a spectral line occurs.
There are number of factors that determine this, but the one of interest here is Doppler Broadening. If an molecule is moving towards you, its spectral lines are shifted toward the blue due to Doppler shift. If it moving away, they are shifted to the Red.
If you are looking at a warm body, its molecules are in motion, moving at different angles t you. All the shifted spectral lines from these molecules blur together to make the spectral line look thicker. The hotter the body, the greater the molecular speeds, and the greater the width of the line.
Thus the width of the spectral lines can give you information about the temp of the Star.
Main sequence stars follow a relationship between luminosity and temp. Hotter stars are more luminous.
Thus if you compare temp and luminosity, and find a low luminosity star with a high temp, or a high luminosity star with a low temp, you know that the star is outside of the main sequence.