Watch the Right Hand String Crossing online guitar lesson by Andrew Leonard from Beginner Method for Classical Guitar
The concept of classical guitar right hand string crossing builds upon the skill of finger alternation. This too is an essential foundational skill.
There are two types: simple and complex string crossing. This video explains both. Exercises follow in the next video.
I believe the phrase "higher and lower strings" is well covered in the video. If it's new to you, below is a brief explanation.
The "high string" (also called 1st string or high E string) is actually the string lowest to the ground. It's called the "high string" because its pitch (or sound) is higher than any other string. When played, it vibrates faster than any of the other strings. The lowest sounding string (also called 6th string or low E string) is furthest away from the ground. It's the thickest string.
Be patient learning new terminology, in time this will make perfect sense. I promise!