Take some object, and place it so that your line of sight is perpendicular (technically, normal) to the front of the object. You see the front of the object only - essentially, a two-dimensional view. If you were to superimpose a grid on the object, it would look like a Cartesian plane:
These are the four quadrants, which you might have heard of in geometry. They begin with quadrant I, in the upper right-hand corner, and then move counterclockwise. Quadrant II is in the upper left-hand corner, quadrant III is in the lower left-hand corner, and quadrant IV is in the lower left-hand corner.
We can say that each quadrant has an angle associated with it: the angle between the two perpendicular planes (for they have depth, not just length) that bound the quadrant.
In a first-angle projection, the horizontal plane from the first quadrant rotates down, extending the first angle to 180 degrees. You then put the view from the horizontal place of the object below the view from the vertical plane of the object. In a third-angle projection, the horizontal plane from the third quadrant rotates up, extending the third angle to 180 degrees. You then put the view from the horizontal place of the object above the view from the vertical plane of the object.
I have to say, this is the first time I've heard the term "second-angle projection". Europe (and Asia, I believe) tend to use first-angle projection, while third-angle projection is common in the United States. Second-angle projection is seldom used.
This pdf has a pretty good (and in-depth) explanation of the idea of projections, and the ones I gave you an overview of.