If you read the glossary, it tells you "The unemployment rate is the percent of the labor force which is unemployed". Well, duh. If you look up "labor force", you get "people who are either working or unemployed". Double duh.
What they don't tell you is that you are considered a "member of the labor force" only if 1. You get a W-2 each January, or 2. are receiving unemployment benefits. The millions of people like me who lost their job but who exhausted their benefits become non-persons as far as that chart is concerned. We're still here - we're still looking for work, but we're not counted either as part of the labor force or as unemployed.
The "household survey" should be considered as well as the "payroll data" when trying to figure out what is going on.
In January, for instance, the number of nonfarm workers on a payroll went from 130,043,000 to 130,155,000 - an increase of 112,000 (seasonally adjusted). The household numbers went from 146,878,000 to 146,863,000 - an increase of 422,000.
IOW, there are roughly 10% more people actually working than are getting paychecks, and in January, the "real" numbers went up almost 4 times what the NYT is reporting.