Can you ask your daughter to explain these terms to you, to learn with her? She may only be explaining them with a basic understanding - there's always more detail and refinement of training to learn about with horses :)
As well as googling, there YouTube and Wikipedia which should have some good detailed explanations and videos about terms.
In brief - An outline is generally used to describe when a horse is properly collected, collection is when a horse is in the correct frame or posture to use itself properly when being ridden.
if you as a human were to try and do a gymnastics routine with a slouched back and hunched shoulders, that wouldn't work and / or would be painful, so you stand straight, slightly bend your knees etc and use your body properly. Imagine trying to do it carrying someone else on your back, and you can only learn how to improve by the person you are carrying communicating through their weight, hands on reins to your head, and their feet, and you can probably start to appreciate why it is difficult and takes so long to train when riding a horse!
What your daughter is taking about are elements of dressage, (don't worry or be put off by the French terms, they are only used as that's where this method of riding was developed) Dressage only means 'to train', so being in an outline is where the rider has to train the horse to collect itself properly to do gymnastic movements as part of dressage (dressage movements are done for training or as part of a dressage test).
Falling is in where a horse, going around on a circle or corner, doesn't bend properly and go around the circle, but instead 'falls in' from the turn. This isn't good as its like not properly using yourself when doing a workout, you won't work out the right muscles or do the movement correctly.
A good resource I can recommend, perhaps for your daughter as well as you, is a website I am using to learn more about dressage, called straightnesstraining.com
I have read and followed the free e book, which explains dressage movements and why they are done. There is a lot of detail if you want to go in to it, but also gives you a basic overview of why horse training is important and what the movements are and how they are trained and ridden.