According to Merriam-Webster's Dictionary, chemistry is "a science that deals with the composition, structure, and properties of substances and with the transformations that they undergo". As explanations go, this is very accurate, if you understand the world of science.
If not, is makes as much sense as the meaning of life being 42.
Let's take it down a notch. Pick a material, could be a piece of wood. It has a color, and when you touch it, you can feel the texture. It also has a odor. If you hit it, e.g. by knocking on it, it gives a distinct sound. If you put it in a fire, it'll most likely start to burn. Now take another material, a stone or a piece of metal. It has another texture, another odor, etc. It may start burning, if you put it in a fire, but it might as well just become very hot. Why? Well, that is chemistry.
Take a piece of material and do something with it, and you've got some chemistry going. Exactly what kind of chemistry we are doing, depends on both the material itself and the surroundings. Did you ever wonder why iron can rust, while gold can't? Did you ever wonder why some people react strongly to being stung by a bee, while others are immune to the bee's venom? Chemistry!
When teaching, you have to focus on very small sections of science, for the students to be able to grasp the information. Due to the way the educational system has been designed, and the history behind it, the scientific disciplines in school have been divided into small sections, each living their own lives, preferably without having anything to do with the other sections. In the real world, it all mixes into science, and the way you focus here is completely different. Here you have a lot of sections working together.
If you look at the classic scientific disciplines, as we know them from school, you could arrange them like this:
| - Chemistry - Physics - Math
Going from left to right, you could say (somewhat simplified) that we are increasing the level of details.
When we have to explain something in nature, we usually start with biology/geology. Why does the plant/rock look the way it does? Why do some animal species become extinct while others survive. Why do some rocks vitrify, while others don't? At some point, as more details are added, biology and geology can't explain what is happening, and you have to switch to chemistry.
Using chemistry you can explain the details, e.g. why arsenic is toxic? Why did the black marble, used for cladding the Black Diamond in Copenhagen, degrade due to the salt used for deicing the roads? When you have described the chemical reactions relating to the biology/geology, you once again reach a limitation. To explain the details in the chemistry, you need to use physics.
Using physics you can explain parts of the chemistry, e.g. activation energy i regards to why paint won't cure if it is too cold or why copper is an excellent electrical conductor. When physics is no longer sufficient, you switch to math.
Math itself is not an explanation, it is a tool for explaining physics and chemistry. It can enable us to understand some of the mechanisms and connections, and it may help predicting mechanisms. In regards to chemistry, math is widely used, e.g. for something called molecular modeling where you simulate the structure and function of macro molecules, e.g. for development of new types of medicine. In principle you could explain the entire world using math, but in practice it would make no sense doing so. It would be the equivalent to downloading the sheet music for a song (i.e. the mathematical representation of the music), instead of downloading the song itself.
The transition between the disciplines is fluid, and many disciplines that we use on a daily basis are somewhere inbetween or include several subjects. Medicine e.g. is chemistry and biology, computers are physics, chemistry and math and ECG measurements of the heartbeat is biology and physics with a dash of chemistry.
This brings us to a very important point, and a misunderstanding that you encounter from time to time, due to the way the educational system works. The math you learn in math class is the same as the one that is used in physics, chemistry, micro economics etc. Physics does not become another type of physics, when it occurs e.g. in chemistry, and likewise, the chemistry you learn in chemistry class will be the same, when it appears in biology and physics class. Even at university level, you see students who can't make the connection that the mathematical equation you see in economics can be solved using the math you learned in math at highschool, because it says economics on the book, and that other thing is math, which is an entirely different class.
It is all connected!