This summer I taught several younger students and I had to explain to all of them about the harmonic series. The harmonic series are the notes you can play on one fingering, most easily illustrated for the notes of the open F horn:
If your horn stands in F you can play all these notes on the open fingering. If you put down the second valve, you will get all the notes a half step lower; first valve a whole step lower, etc. If your instrument stands in B-flat you can play all these written notes on the fingering 1-3 (which is the same length as the open F horn), a half step higher would be 23, etc. A little experimentation will quickly show how it works.
The higher you go, the trickier it is to be accurate
I was exposed to the concept of the harmonic series pretty early on in warm-up materials from my first teachers.
Not every teacher has students do harmonic series studies. I feel they are valuable; if exercises on the harmonic series are unfamiliar to you get a copy of Farkas, The Art of French Horn Playing, and work on the materials in his warm-up. Just about every book on horn playing has some exercises of this type.