We've been talking about graphs in class and my understanding is that $K_3$ means a graph $K$ has $3$ nodes. I have also been reading online to get a better understanding of what was said in class but then I came across multiple examples and blog posts talking about $K_{3,3}$
So my question is, what does $K_{3,3}$ mean? is it simply saying $6$ nodes?
$K_3$ refers not just to any graph with 3 nodes (vertices), but rather to the complete graph on 3 vertices. See here for more information about complete graphs.
Meanwhile, $K_{3,3}$ refers to something called a bipartite graph. This is a graph for which the vertices can be separated into two sets, such that all of the edges cross from one set to to the other. See here for a precise definition and more information about bipartite graphs.