What is the 'centre of gravity' of an object and how do I calculate it?

The centre of gravity (or centre of mass) of an object is the point through which an object's weight will act through. In other words, the object will always balance around this point.

Imagine a square book; the centre of mass of the book is where the lines of symmetry of the book meet. As it is a square this is right in the middle of the book. Position the book on the edge of a table and it will only tip over the edge once this point is no longer in contact with the table. 

In order to find the centre of gravity of an object, simply hang the object freely from a corner. Using a plumb bob for reference, draw a vertical line downwards from the point of suspension. Repeat this process for at least two more corners, and the point at which the lines intersect is the centre of gravity.