Your instructor is your best source of information on these things. If you don’t ask questions, your instructor will not know that you need more explanations.
There are two different kinds of knowledge gaps in riders.
It’s possible you are a competent rider with good balance and timing, but you didn’t take formal lessons as a kid, and so missed learning some of these fine points and terms. But if you look like you can ride, people might be expecting that you must also know these points. For instance, when I went back to riding lessons as an adult, I did not know what a 20 metre circle was 
though in fact as a teen I had taught my pony flying lead changes riding circles and figure eights.
On the other hand, it’s also possible that you are still struggling with balance and timing.
I would say the solution to both possible situations is the same. Book a private lesson with your coach. Have her go through all the moves used in your group lessons, and determine if (a) they are within your skill level, you just need some clarification on the terms and techniques or (b) they are not within your skill level and you need to move down a level.
As far as books, there are many books on basic equitation out there. Visit a local tack store to browse. There are also many videos. But the problem with trying to learn a physical skill from a book, is that the idea you get from the printed word may be totally different from what the instructor wants.
Here are some on-line glossaries:
http://www.dressage-academy.com/dressage-glossary.php
http://www.statelinetack.com/statelinetack-articles/horseback-riding-terminology-for-beginners/10076/
https://en.wikipedia.org/wiki/Glossary_of_equestrian_terms#H
http://www.nodarider.org/education/dressageterminology.pdf
I don’t know how useful these will be to you.
There is a lot of variation between what different instructors mean by terms like “half halt.” You can start Googling this if you want to see what I mean :).
As far as “reflection,” that’s not a term I have ever heard used in regards to riding, so you must have misunderstood.
Your instructor should be your guide here.
