We observe a distant object in space and see that the spectral lines for hydrogen in the object's light appear at a shorter wavelength than normal. What does this tell us about the object

This tells us the radial velocity of the object and that the object is approaching or coming towards us.

Explanation:

Certain chemicals radiate with particular wavelengths or colors when their temperature is raised or when they are charged electrically. Also observable are dark strokes separating the spectrum known as absorption lines

These spectral lines of chemicals are well known as stated above and from the phenomenon of Doppler effect, spectroscopy can be used to detect the movement of a distant object by the change of the emitted frequency of the wavelength

The Doppler effect is used in calculating the radial velocity of a distant object due to the fact that an approaching object compresses its emitted signal wavelength while a receding object has a longer wavelength than normal