I think it means letting the transformed image depend (in part) on the derivative of the signal and so making it easier to detect features like contours. The eye is known to be very sensitive to  local contrast, making the light bordering a dark area seem lighter and a the dark seem darker, and allowing you to see details in the shade even though the luminosity in the shade is much much lower than in the sun.  have a look at  https://en.wikipedia.org/wiki/Contrast_(vision)

You can do it algorithmically by using a convolution filter based on the derivative of a gaussian, The references below  for example, should give you an idea.  

http://arxiv.org/abs/1208.6223

http://www.diva-portal.org/smash/get/diva2:452310/FULLTEXT01.pdf

Histogram Equalization is a global operation. For local contrast enhancement, you can do block processing of an image i.e., divide images into blocks. For each block, based on the statistical properties suitable contrast enhancement routine can be applied

Dear R. Prasad,

Use adaptive histogram function of Matlab which enhance the contrast of image by dividing it in small blocks. Syntex of the function is [output = adapthisteq(input)].

Description of this function as provided in Matlab is here:

adapthisteq: performs contrast-limited adaptive histogram equalization. Unlike histeq, it operates on small data regions (tiles) rather than the entire image. Each tile's contrast is enhanced so that the histogram of each output region approximately matches the specified histogram (uniform distribution by default). The contrast enhancement can be limited in order to avoid amplifying the noise which might be present in the image.

see page 4 to get a  idea related to your project

Local contrast enhancement is needed whenever we are concerning with images containing very sensitive information like satellite images. In such cases, rather than considering the whole image at a time, we go for considering a single tile and apply the enhancement technique on it, and this process is going on until we cover all the blocks of the image. So, when you are going for local contrast enhancement, you can apply any available enhancement (like histogram equalization) , but it should be on the specified tile at a time. I suggest you  apply any CLAHE based technique for the same as I myself found it very efficient in some of my research work. But, it is to be noted that sometimes, local contrast management may enhance the contrast of  noises also.