Imagine you are standing somewhere in a vector field. If you move slightly in a particular direction, the field changes and the change is dependent on the field and the direction in which you are moving. If for every individual point you sum over all those relative changes in every direction, you get a scalar quantity that reflects the extent to which the field diverges outwards in that particular point. The resulting scalar field is aptly called the divergence of the vector field. A point with a positive divergence can be seen as a source of the field and a point with a negative divergence as a single of the field. Know that you have lost any directionality that was in the initial vector field. It is impossible to go back from the scalar field to the vector field. In particular, the divergence plays an important role in the divergence theorem, causes law and is magnetic equivalent.