What does the term "proportional to" mean in Bayes Equation?
It means that $P(\theta | y ) = kP(\theta) P(y | \theta)$, where $k$ is a constant that does not depend on $\theta$. 

In fact, the Bayes Theorem states $P(\theta | y ) = \frac{P(\theta) P(y | \theta)}{P(y)}$. This proportion has to be added in order that $\sum_{\theta}P(\theta | y) = 1$ is satisfied (that is, $P(\theta | y)$ has to be a probability).