It means that every year, your boss calls you into the office and gives you a small pay DECREASE. Wages go down. Even though the relative spending power of your lower wages might stay the same (i.e. your lower wages buy the same number of Big Macs because the costs of Big Macs drop as well). That is not good for moral for workers to get pay cuts every year.

Though this conversation can happen, wage stickiness is a problem. Most people (or their employment contracts) won't allow a pay cut, so it turns into a mix of falling company profitability and/or layoffs. This in turn leads to these same things you note: less hiring, lower aggregate demand, and so on down the drain. It's economically rational to prefer a pay cut to getting sacked, but things don't usually work out that way.

Random blathering:

Wage stickiness is one of the reasons for having an inflation target of (say) 2% instead of zero. At any given time some companies and industries are fading, and it makes sense for their workers' compensation to fall gently. People don't like nominal pay cuts, but just a bit of inflation greases the wheels to achieve what's needed. The real pay is truly getting cut slowly, but in a way that does not cause rioting. At some point the employees move on to greener pastures, with or without the failure of the firm, and on average that will be into growing industries.

The words "on average" have a lot of work to do. Some people get the muddy end of the stick, being unable to get positions in those growing areas, but there is no cure for that yet. Overall, it's better for the world for unprofitable business units to wind down and shed workers. Ask Horatio Hathaway.

Jim