So firstly, we need to work out the basic shape of the molecule which we can do by drawing the lewis structure (dot and cross diagram) and counting the number of charge clouds around the central atom. In the case of ammonia there are 4 charge clouds (3 bonding pairs and 1 lone pair) so the basic shape of ammonia is tetrahedral and the bond angle is 109.5 degrees.
However, as you can see there are 3 bonding pairs (nitrogen bonded to hydrogen) and one lone pair of electrons (unpaired electrons on the nitrogen). The lone pairs distort the shape of the molecule because they're closer to the nitrogen and therefore repel more than bonding pairs of electrons. So the bonding pairs of electrons are pushed as far apart as possible in order to minimise repulsion. Therefore, the actual shape is trigonal pyramidal with a bond angle of 107 degrees.