Can anyone please explain the the difference between a vector and a matrix?

Very roughly speaking ...

A matrix is a 2-dimensional rectangular array of numbers. If the array has $m$ rows and $n$ columns, we say that we have a matrix of size $m \times n$.

A vector can be regarded as a special type of matrix. A row vector is a matrix of size $1 \times n$, and a column vector is a matrix of size $m \times 1$.

You probably know how to multiply matrices. Since vectors are just special types of matrices, you know how to multiply a matrix times a vector. Multiplying by a matrix is often used as a way to somehow "transform" a vector (to rotate it or mirror it or scale it, for example).