Confusion about optic axis

When you travel (on a straight line, with an associated vector) in the western direction, that doesn't mean that you travel on one single line to travel on.
On the other hand, if you travel on a straight line you always travel in one direction. One can say that a direction is a continuous collection of straight-line pieces (with equal lengths and the same origin) and that it's somewhat arbitrary to define the boundaries of these collections. The average of all these pieces though is a single line starting at an origin and having a non-zero length.
You can travel the same length on a straight line from where you start (the origin) to all points around it within 180 degrees. The average will be a line-piece emerging from the origin where you started with a certain value.
If you change the boundary to 90 degrees you'll obtain a similar line-piece than in the 180 degrees case but the piece will be longer though.
The same holds, more or less, for the optical axis as mentioned in your book. The straight line-pieces are infinite though and passing the origin at the center of a lens (presumably).