It is easy to understand angular size by imagining that you standing some distance from some kind of large landmark, like the Golden Gate Bridge. Hold out your arm and point to one end of the bridge, then - without moving your arm - turn your body slightly so that you are now pointing to the other end of the bridge.
How far around did you have to turn? 5 degrees? 10 degrees? 90 degrees? That is the angular size of the landmark from your location.
Of course, the closer you are to the bridge, the more you will have to turn to point your arm at either end. Angular size depends on how close you are to the object you are measuring. This is why angular size is useful in astronomy - with minor exceptions, everyone is the same distance (give or take the tiniest fractions) from the objects being measured.
While angular sizes measured in degrees are useful for larger patches of sky (in the constellation of Orion, for example, the three stars of the belt cover about 3 degrees of angular size), we need much finer units when talking about the angular size of galaxies, nebulae or other objects of the night sky.
Degrees, therefore, are subdivided as follows:
360 degrees in a full circle 60 arc-minutes in one degree 60 arc-seconds in one arc-minuteTo put this in perspective, the full moon viewed from earth is about 1/2 degree, or 30 arc minutes (or 1800 arc-seconds). The moon's motion across the sky can be measured in angular size: approximately 15 degrees every hour, or 15 arc-seconds per second. A one-mile-long line painted on the face of the moon would appear to us to be about one arc-second in length.