The BLS first included alternative measures to the U-3 rate in 1976 to allow people to see the unemployment situation from different angles.
If you're wondering which number you should trust, the answer is both. U-6 and U-3 measure different things.
Here's the difference: the BLS classifies an unemployed person under U-3 as someone "without work, available for work, and [who] has actively searched for work."
The U-6 rate is the BLS' broadest measure of unemployment. It includes people not "actively" looking for work — referred to by the BLS as the "marginally attached," meaning people are unemployed but have not looked for work in the past month because they got discouraged and gave up. U-6 also measures the number of people who aren't able to find enough work, i.e. people who are working part-time when they want to work full-time, called the "under-employed".
The U-6 rate is now at its highest level since the alternative unemployment measures were revised in 1994.