what is gradient?

I saw the term used in a paper, but really cannot remember what it is and what it means. Forgot too much about those basic mathematic concepts...

 

Here is from wiki: http://en.wikipedia.org/wiki/Gradient

 

Another is a Chinese website which helps a little: http://sxyd.sdut.edu.cn/gaoshu2/lesson/8.7fangxiangdaoshuyutidu.htm

 

Now it is time to see what it means in the paper...