Altitude describes the angle between the nearest part of the horizon and a star. Azimuth describes where around the 360° horizon you can find the point to look up from. That is azimuth is the angle from the north point on the horizon to the foot of the vertical circle that goes through the star. The altitude of the north celestial sphere here at CSB/SJU is 45°, its azimuth is 0°.
The above shows vertical circles labeled with their azimuth. The vertical circles, of course, would all meet at zenith. Notice that the belt of Orion has an azimuth of about 135°, and hence should be seen directly above (i.e., on a vertical circle through) the SE point on the horizon.