This is in your Theme’s stylesheet. You might check first to see if your Theme has options where you can just change a color setting.
If not, and if you’re not familiar with editing CSS, then I wouldn’t recommend tackling it until you learn more about CSS, you’re better off to post in the support forum for the Theme Developer to ask for help there.
If you can’t get help and decided to try modifying it yourself, your stylesheet is under Appearance>Editor, but copy it all and paste it to a text file on your computer and save it before you do anything – that way if you mess up you can paste it back to the way it was.
When you view your site, you should be able to right-click and choose “view source code” – this will help you identify the classes for your menu items.
In your case, there is a DIV with a class of “main-nav” in which you have an unordered list (ul) with a class of “menu” and list items (li) for each menu item. You’ll find those in your stylesheet and can try adding a gray background (background:grey;).
As for adding space, keep in mind that you’re using a responsive theme and adding space may cause unexpected consequences on other devices, but that would be a margin, which can be expressed in terms of .ems or pixels, or percentages. I would suggest using a small percent on the right side margin of each list item (margin-right:1%;)
I hope this helps – if it sounds like greek, I’m sure the Theme Developer will be able to better advise you. A good resource to learn about CSS is SitePoint (their reference site):
http://reference.sitepoint.com/css
Good luck!
