While it’s generally good to position the subject so the background is out of focus, the background is an important part of the close-up shot. In most cases, it helps tell part of the story—giving some context to the subject.

In the top shot on the right, the people in the background imply it’s a public place, perhaps a bar or restaurant. And the 1950s clock gives viewers a sense of the time period.

In the lower shot, the mountains immediately give the viewer a sense of the location.

In both cases, the backgrounds don’t distract, but they do provide a bit of context.