I am new to blender. when I try to move a vertex in a mesh instead of simply moving the vertex it creates a new cell, how can I disable this option so that when I drag the vertex it should easily move to the new location without creating a new cell.
Are you extruding individual verts to create geometry and filling them using Fill command?
This normally happens when there are duplicate verts created when this method is used.
Selecting all verts and removing doubles will remove any duplicate verts and will not create any additional geometry when the space between the verts is filled.