Here, I'll explain the 7 Hermetic Principles from The Kybalion in the way that I understand them. Please read or listen to the whole thing if you get the opportunity, but this is just a sort of Cliffs Notes version.
Mentalism Essentially, this is the idea that everything in existence is a mental creation of what the text calls The All. The All refers to something like energy, life force, spirit-- it's the thing that connects us all and it's where we "came from." This is accepted in the text as the explanation for why some things seem to be universal even across vastly different cultures.
Correspondence This one should be familiar to anyone who's studied magic. "As above, so below." If there are unknown forces and planes, we should be able to apply logic similar to our own world in order to understand them.
Vibration Everything vibrates. Nothing is truly still. This is technically true, as we have learned over time about atoms and how each one is made of a bunch of tiny rotating pieces. Different items have different vibrations-- some have faster movement (higher vibration) and some have slower movement (lower vibration). The only atoms that could potentially stop moving at all would be at 0 Kelvin ("Absolute Zero"), a theoretical temperature that has so far not been achieved. From the text: "The vibration of Spirit is at such an infinite rate of intensity and rapidity that it is practically at rest--just as a rapidly moving wheel seems to be motionless. "
Polarity Opposites are actually just different degrees of the same thing. "Heat" and "cold" are just different degrees of temperature. "Love" and "hate" are just different degrees of emotional attachment. You get where I'm coming from? Even though we think of these things as being completely different from each other, they really are the same sort of thing. There are extremes and middle-grounds. "Neutral" is achievable with all of these. Room temperature is neither hot nor cold. Disinterest is neither love nor hate. Thinking of it this way, it becomes possible to "shift" how you feel about something. Are you sad? Sadness and happiness are different degrees of the same emotion. With some time and effort, you could start to see how sadness slowly works its way over to happiness.
Rhythym This one builds nicely off the last one. Everything changes. The pendulum swings back and forth at roughly equal rates. This is perhaps most easily explained with the seasons. It's really hot, then it cools down, then it's really cold, then it warms up until it's really hot again. The plants go dormant and come back. The birds migrate and come back. The same can be said of our minds. Our emotions go back and forth. Our health goes back and forth. Our thoughts go back and forth. Once this is understood, with some work, we could potentially use this information to our advantage.
Cause and Effect Have you ever heard "everything happens for a reason?" Take that to the Nth degree. There's no such thing as chance. Everything happens because something caused it to happen. Humans are affected by things that happen on the "higher planes." If you can figure out how to tweak things on the "higher planes" to your liking, you can cause your own effects.
Gender This one is going to seem a little outdated. A lot of things in mysticism are explained as being "feminine" or "masculine," but it's probably more accurate to call the feminine things "gentle/receptive" and the masculine things "intense/influential." The sun is intense/influential/"masculine" because it creates and pushes out light. The moon is gentle/receptive/"feminine" because it doesn't create its own light, but instead receives and uses the light from the sun. The world needs both of these extremes as well as everything between them (see "Polarity" above). The balance is incredibly important.
So, there's the basic idea of the 7 Hermetic Principles. Hopefully this helped make it a bit easier to understand. I might edit later to add more information or to clarify a point.