In the context of fluid mechanics, where a given vector field is interpreted as a model of a fluid, with the vector value at a given point being the velocity of the fluid particle at that point, curl and divergence are used to express notions of rotation and expansion/compression of a fluid, respectively.
So, for example, if the divergence is positive at a point, it means that, overall, that the tendency is for fluid to move away from that point (expansion); if the divergence is negative, then the fluid is tending to move towards that point (compression).
Curl is a little more involved than this. The direction of the curl vector suggests the axis around which a particle immersed in the fluid at a fixed point (but otherwise allowed to rotate freely) would rotate in an anticlockwise direction, provided its rotation is only due to the aggregate effect of contact with the fluid immediately around it; the maginitude (modulus) of the curl vector is then the speed at which it rotates.
you can have a look in this site for better understsnding.....you can use mouse to interact with the animations....the url is http://www.math.umn.edu/~nykamp/m2374/readings/divcurl/