Determinants and matrices are a topic of linear algebra, so their significance lies in linear equations.

Take the system of linear equations:
$$a_1x+b_1y=c_1$$
$$a_2x+b_2y=c_2$$
In matrix form, this is the same as
$$\underbrace{\begin{bmatrix} a_1 & b_1 \\
a_2 & b_2 \end{bmatrix}}_{A\ \text{(let)}}
\begin{bmatrix} x\\y\end{bmatrix}=\begin{bmatrix}c_1\\c_2\end{bmatrix}$$
Now, whether or not they have a unique solution is determined by the number $a_1b_2-a_2b_1$. (You're in high school, so I assume you know how to solve linear equations; if you don't know, then you can learn! Comment, I will add some more info on that) So, we define this number to be the determinant of the matrix $A$, denoted by $\det A$ or $|A|$.

We can then generalise and utilise this method to solve *any* system of linear equations. You'll learn this later on in the same topic (at least I think).

Hope this helps. Ask anything if not clear :)