If you google this question "What is linear Algebra?" you will probably get a couple of different and very "mathematical" answers to this question. The way I like to think about it is that linear algebra is a branch of mathematics that deals with vectors, matrices and systems of linear equations.
So what, why is this important for machine learning (ML)?
To understand this, lets look at the definition of a vector. Depending on your background, if I say vector you might think of if in different ways.
If you are into Physics you will probably think of a arrow pointing in space.
If you are a software engineer, you will probably think of a ordered list of numbers.
Lets say you wanted write a script that performed analysis on the housing market. In this example the only data you care about is the size of the house and the price. You would probably use a vector to store this information.
You would then have to perform some operations on these vectors (add or multiple). This is why understanding linear algebra is important for ML. When working with data in ML you will more than likely be using vectors and matrices as the data structures of your programs and understanding how to manipulate these is very important.