Angular measurements are based on the concept of dividing a circle into 360 parts (called degrees).  Angular sizes are used to estimate diameter of an object.  Both the Earth's moon and the sun have an angular diameter of one-half degree.  A general rule of thumb is that your index finger held at arm's length (with a straight arm) is approximately 1 degree wide, while the length of your fist held at arm's length (with a straight arm) is approximately 10 degrees wide.
 

Azimuth refers to the compass direction that you are facing.  North is assigned an azimuth of 0 degrees. Azimuth numbers increase from north in a clockwise direction.  For example, if you saw a fireball straight in front of you and you are facing halfway between due east and due south, then you see the fireball at azimuth 135 degrees (halfway between 90 degrees and 180 degrees).
Altitude refers to the height above the horizon and goes from 0 degrees (along the horizon) to 90 degrees (directly overhead).  Altitude will always be between 0 and 90 degrees.  If you saw a fireball that was about 1/3 of the way up from the horizon to overhead, then it would have an altitude of 30 degrees.