What would mining whole chunk mean?

A single chunk is A 16 X 16 area 256 blocks deep. It is probably saying to mine a 16 x 16 area at the level diamonds appear.

As far as I am aware this will not certainly get you diamonds. You are probably better off looking for dirt at the levels diamond exist and mining all of the dirt as diamonds can appear among it.

For diamond mining tactics check out the wiki. http://minecraft.gamepedia.com/Tutorials/Diamonds

This tip is using the crawl feature. Mine one side of the outline of a chunk (just the levels that diamonds spawn)(or you can do 9-12 y to be more efficient, then do multiple chunks), as it has a guaranteed number of diamonds that I forget, then on that side, use the crawl feature with a trapdoor or piston and mine like the following graph. # is a mined strip, 0 is a non-mines strip. as you can see, you look at every block in the chunk, while mining only just under a third of the blocks in the chunk or area. This is of my own design though.

#000#000#000#000#000#000# 00#000#000#000#000#000#00 #000#000#000#000#000#000# 00#000#000#000#000#000#00