I looked up what this proverb is. It is: While the grass grows, the steed starves.
This is explained as if you wait too long, dreams may not be realized. I’m not sure this makes sense to me. It makes sense as it relates to Hamlet, sure –
But on its own. . .
Why is the steed starving? Do steeds not eat grass?
Is it that they eat hay – like, dried grasses?
I don’t know – it just seems like, if the steed is hungry, it’ll just eat whatever it can find, if the grass is to its taste or not. I’d eat grass if I were starving.
But. . .this proverb is VERY musty. It’s very probable that this was a well used proverb at the time – one every one could complete after hearing just the grass growing part. Modern audiences have to make up what the rest of it might be.
I think I imagined it was something like, “While the grass grows, the sun shines everywhere.” I wanted it to say something about glory going on without a person (or the grass. . .) so the actual proverb is a little bit disappointing compared to the one in my imagination.
Something musty indeed. Something musty in 1599, 1601 or so, is EVEN mustier here in 2016.
The Hamlet Project 
I’d suggest that the phrase actually means that one must hasten in action and be the maker of ones own fortune. Think of yourself as the steed; you watch the grass grow and think ‘all is plentiful, I have all the time in the world’ but if you never take a bite, you will starve. In this way, Hamlet is remarking that although he is next in line for the throne; he knows his Uncle is usurper and he must act with haste to avenge him father. That Hamlet forgets the end of the saying is Shakespeare wittily noting that perhaps even now, Hamlet is too late in his action, time is running out.