How are matrices related to vectors? I know it's a silly question, but there's something I feel like I'm missing in my understanding of matrices. 
I'm studying linear algebra, and much of what we covered in the first few topics related to vectors (vector spaces, linear independence, etc.), but then all of a sudden we started using matrices, loosely defining them as an "array of numbers". 
So I'm kind of confused, is a matrix supposed to be a list of vectors? And if so, are they the rows or the columns of the matrix? 

Have you started multiplying matrices and vectors yet? If so, one can look at it from a more abstract point of view. Informally, if we take the set of all vectors with $n$ entries, we can look at the kind of mappings from that set to itself. That is, we want to find a function that takes a vector with $n$ entries ($\mathbb{R}^n$ if you are working with reals) as input, and outputs another one with $n$ entries$^1$. This is a large set of functions, so we might want to restrict to a certain class of functions. In particular, if we limit ourselves to functions that are linear, it turns out that the only remaining functions are exactly those that correspond to multiplying a vector with an $n\times n$ matrix! This gives us a nice relation between vectors and matrices, matrices map vectors linearly to other vectors, and multiplication of matrices then corresponds to composition of linear mappings.
$^1$More general, something similar also holds for mappings between any $\mathbb{R}^n$ and $\mathbb{R}^m$.  
