Meditations influence is covered in depth in The Willpower Instinct, but here's a short summary.
""Meditation requires you to tap all the self-regulation systems in your brain as well as the self-monitoring mechanism," says Kelly McGonigal, PhD, a health psychologist at Stanford University and author of the forthcoming The Willpower Instinct. Every time you meditate, you use two important parts of your brain: the prefrontal cortex, which helps you make smart choices, and the anterior cingulate cortex, which helps you be aware of when you make such choices and when you don't. The more you activate these systems, the more powerful they become, so in the future it will feel easier to do the right thing. "Eventually you will start to notice whenever you are doing something that is inconsistent with your goals," McGonigal says."
But these studies are on noticing structural changes, not changes in the subject's capability.
What makes meditation better at this than, say, sitting down and doing math homework or going out and doing exercise? There's a lot of research to strongly correlate regular physical activity with intelligence (random googled summary with many citations here: http://www.unm.edu/~lkravitz/Article%20folder/brainandex.htm...).
https://www.google.com/search?q=willpower+muscle+research
More interestingly, there is research that suggests that believing that willpower is like a muscle impairs willpower. :)
http://pss.sagepub.com/content/21/11/1686