Clout, along with a units level determine the Unit Quality. The higher a Unit Quality, the better the Unit chassis that can be used.
The only way to take advantage of all of the units the game has to offer is to put enough stat points into Clout. It is factored into your Division Influence as Clout/2 + Division Level. So, if you have 20 Clout and are level 2, your division influence will be 20/2 + 2, or 12.
Note: This table assumes that all units are level 60, since you'll get there eventually, and that's when clout really matters. There are no units on UQ (Unit Quality) levels 6, 8, 9, 11-13, 23, 37, 41, 51, 69, 79, and 111. Table courtesy of CheesePony (http://www.jerekdain.com/). Added by JimRaven.