Do these leaves signify anything?

Yes, the rustling leaves usually indicate that there are pokemon near that area. Going and walking around near that area gives you a higher chance to encounter Pokémon.

Keep an eye out for rustling leaves, hinting at where critters may be lurking and simply hang out in a suspected region for the increased chance of an encounter. - Source

Edit:

I've been running and testing the leaves thing for a bit, and even though there have been reports that it increases the odds of finding Pokémon, I personally find using the step indicator to be far more reliable. An additional benefit is that you can actually use the steps to select a Pokémon you want to catch, and specifically go after that one. Here's how:

Step 1: Open up the nearby list and decide which pokemon you want to find.

Step 2: Keep walking in a direction until you see that pokemon move a spot in the list. If it moves closer to the upper left corner, you're walking towards that pokemon, so continue walking that way. If it moves down the list, backtrack and choose another direction to walk in.

Step 3: Continue to triangulate until you find your pokemon (also pay attention to the 'footsteps' underneath the pokemon, these should go down from 3>2>1>none).

Step 4: Benefit.

Source

I believe these mechanics (steps + leaves) could possibly be meant to be used together to track down Pokémon the most efficient way. Use the steps to get a general bearing of the target location, then look around for leaves to home in.

I've had a Wartortle spawn inside the leaves before, and I believe the leaves are an indicator of a possible Pokémon spawn point. This does not mean that Pokémon are currently at that location, just that Pokémon spawn (and despawn) there - based on my findings and players I've spoken to.