What is an (electrostatically) induced charge?

When an electrically charged object (e.g rod) charges an uncharged object (e.g. metal sphere) that is nearby with the opposite charge. 

How does this happen?

The charged rod causes the charges on the sphere to be redistributed.

For instance, if the rod is positively charged and is brought near a point A on the surface of a sphere, a negative charge will accumulate at point A inside the sphere. This occurs because electrons inside the sphere are attracted to the rod and are free to move across electrically conducting objects.

*Important to note that the total charge of the sphere does not change.