The square head is arguably the most commonly seen part of the combination square set.
It is traditionally used for determining whether angles are at right angles or 45 degree angles (such as a 45 degree mitre in a mitre joint).
For this purpose, it has one edge which rests at right angles to the rule…
…and one which rests at a 45 degree angle to the rule.
It can also be used when marking an object (such as a plank of wood) for cutting…
…and when measuring depths (e.g. depths of grooves/channels).
As mentioned above, one edge of the head can be used to measure 45 degree angles, but the same edge can be used to measure 135 degree angles as well.
Contained within many square heads is a “scriber” (sometimes referred to by variants such as “scribing tool”), which can be used to make marks on objects.
This is particularly useful when working on metal, where pencils would be useless.
In addition, square heads normally have a spirit level built in.