What is meant by a "sodium line"? 
What speed should a galaxy move with respect to us so that the sodium line at $589.0\ \mathrm{nm}$ is observed at $589.6\ \mathrm{nm}$?  

In the above question what's meant by a sodium line?
The question is related to the Doppler effect.
I searched the web for "sodium line" and got results for sodium lamp. I know that sodium light has been used here but I am not understanding what a sodium line is.
 A: The sodium line that is being referred to is a reasonably sharp, dark absorption feature that is seen in the orange part of the visible spectrum of the bulk of stars that make up the light from a distant galaxy.
The absorption is caused because stars are hotter in the middle than they are on the outside. The relatively cool gas on the outside has sodium atoms in lower energy states, and these are reasonably opaque to photons of particular frequencies that excite them to higher energy levels. Because the outer atmosphere is usually in equilibrium, the excited atoms do re-radiate photons at these frequencies, but in all directions, so that light is removed from the original beam.
In cool stars like the Sun, the sodium lines (a good spectrograph will show you it is a doublet, separated by 0.6 nm, caused by LS coupling in sodium atoms) at 589nm is one of the most prominent absorption lines. Because stars like the Sun and cooler usually form the bulk of the light seen from a galaxy, this line is easily seen in galaxy spectra, and the difference between it's wavelength and 589nm can be used to estimate the redshift (or occasionally blueshift) of galaxies.
As for why they are called "lines" - I think this is just historically how they were first detected. When a photographic spectrum of the Sun is obtained it is usually in the form of a strip, with wavelength along the x-axis. The absorption lines (not just sodium, but others - Ca, Mg and many others) appears as sharp, dark stripes in the vertical direction - and were originally called Fraunhofer lines.
A: The emission spectrum of sodium contains two very bright yellow lines called the D lines. Since they are so bright and so easily seen they are something of a favourite for spectroscopic studies.
In this case the question is referring to the D1 line, which has a wavelength of 588.9950nm (the D2 line at 589.5924nm is only half as bright as the D1 line). The question is asking you what velocity is required to Doppler shift the D1 line to a wavelength of 589.6nm.
A: It is a standard line in the atomic spectrum of sodium, that is used as a standard 

The line you refer to in nmeters is a standard line because of its strength for determining refractive indices of materials in the lab.

A reference wavelength of 589.3 nm (the sodium D line) is most often used. T

The evolution of the line due to the motion of the originating source using the appropriate equations  can give the velocity of the stellar body and the way it changes. 
