"Hysteresis" is a funny-sounding word for a funny-sounding problem—when a spell of cyclical unemployment goes on for a long time, the structural level of unemployment goes up.
The reason this happens is that matching workers with jobs isn't a trivial task. If a single parent or both adults in a two-parent household are going to work, there needs to be child care arrangements for the kids. Firms with openings need a way to communicate the existence of job openings to potential applicants and then screen them in an efficient way. Yet as high unemployment persists, the tendency is for these matching functions to wither away. And that's the right way to understand Nelson Schwartz's piece about companies increasingly relying on internal referrals to fill new positions, thus locking the long-term unemployed and those without connections out of jobs.
After all, running a recruiting operation is a cost of doing business. If you're able to fill all the jobs you need filled without running one, then why bother? If the unemployment rate were 5.5 percent, then the point of running a recruiting operation would be that it's cheaper than constantly offering everyone raises so that nobody ever quits. But when the unemployment rate's been lingering above 7 percent for years, it makes more sense to focus on cost-cutting rather than expanding your labor pool. But as companies disinvest in recruiting functions, people who are isolated from the labor market become even more isolated.