As with any printed media, you'll really have to see the print to check if your colors match the design, and unless you're an expert with print, there's a good chance you'll want to run a copy, revise a couple of colors, and print again.
CMYK can really only get so close to matching what you'd see on paper vs what you'd see on screen since there're so many printers, inks, and different substrates out there.
100% key rarely results in black, rather it comes out in dark grey. That is, depending on the substrate, but it's safe to assume most materials will result in dark grey. Sometimes even having an ugly yellow/greenish hue* to it.
You'll want to look into printing true black. True black, refering to actual black, or as close as you can get to it, is accomplished in CMYK by adding some additional color (lets think of colors more in terms of inks)... ..additional inks to your black. So instead of 100% key, 0% Cyan, 0% Magenta, and 0% Yellow, you might have 100%k - 20% cyan - 31% magenta. It's a tricky process you'll have to fiddle with some. The article I linked to explains it in more detail with some graphics that should clear this up for you.
The light grey is really just photoshop trying to tell you that's what it's going to look like with the current CMYK colors after being printed.
*In the case of printing on newsprint, such as Newspaper ads or inserts they will nearly always request 100% K. The rich black will bleed on that paper, and be difficult to align. The output of using rich black is often out of balance and blurry.