The most obvious way in which sticky wages impede employment is by keeping the cost of hiring workers above the equilibrium wage. The standard story explains that sticky wages increase unemployment. The standard story, however, is not the only and perhaps not the most important transmission mechanism.
Wages are the largest component of costs thus sticky wages keep costs high and profits low. The point is obvious once stated but it has implications for how we look at sticky wages. Tyler, for example, writes:
[Consider] illegal immigrant Mexican construction workers, a group which lost jobs in large numbers following the crash. Are they — who often came from $1 a day environments — also supposed to have sticky wages? They are out of work in massive numbers.
The focus here is on the unemployed workers with the argument implicit that it's the stickiness of their wages which counts (which makes sense given the standard story). But suppose that the problem is that firms can't get capital to expand–perhaps because the banking system is not working well–then what matters for firm expansion is free cash flow. But sticky wages keep firm costs high, reducing free cash flow and inhibiting expansion. In this argument, the stickiness that matters is the sticky wages of the employed workers.
A story which focuses on employed workers has several advantages. First, the wages of employed workers are clearly more sticky than the wages of unemployed workers–in fact, if you are employed real wages are up slightly. Moreover, since more than 90% of workers are employed this type of argument has leverage.
If there are fixed costs, new firms do not arise instantly so infra-marginal sticky wages can be important for a number of "balance-sheet" reasons in addition but related to the free cash flow story such as debt constraints or various coordination and risk reasons.