In Preview
Open the image in Preview and click the Remove Background button in the toolbar, or press ⇧⌘K. The people or things in front stay, and the background is taken away.
If Preview asks to convert the image to PNG, you can click Convert to change the original. To keep the original as it is, click Cancel, choose File › Duplicate, and remove the background from the copy. To go back, choose Edit › Undo.
In Preview on macOS Sequoia or Sonoma
Apple’s guide for these versions uses Instant Alpha, which takes away areas of one color. Show the Markup toolbar if it’s hidden, then click Instant Alpha and drag over part of the background. Preview selects it and the pixels around it of a similar color. Press Delete.
To remove everything outside what you selected instead, choose Edit › Invert Selection, then press Delete. Repeat until the background is gone.
In Finder, with a Quick Action
Select the image in Finder or on the desktop, Control-click it, and choose Quick Actions › Remove Background. The same Quick Actions are at the bottom of the Preview pane in a Finder window. If you don’t see the pane, choose View › Show Preview.
If Remove Background isn’t in the menu, choose Quick Actions › Customize. Extensions settings opens, where you can add it.
Just the subject, from Photos
To copy only the subject of a photo, open it in Photos, Control-click it, and choose Copy Subject. Then paste it into a document, an email, a message or a note. To send it right away, choose Share Subject instead.
The same works in Safari, Quick Look, Mail and other apps.
By dropping it on the notch, with Tilora
With Tilora, drag the photo to the top of the screen. The notch opens into four places: the Shelf, Transform, iCloud Drive and AirDrop. Drop it on Transform and choose Remove Background. The cut-out copy is saved beside the original, which stays as it was, and goes on the Shelf, ready to drag into a document or a message.
It all happens on your Mac, with the Mac’s own frameworks; nothing is uploaded. More about the file shelf.
Questions
Why does Preview ask to convert to PNG?
A JPEG can’t have a see-through background, and a PNG can. Converting changes the original file, so choose File › Duplicate first if you want to keep it.
Does removing the background change my original?
In Preview, it can, if you convert the original. Copy Subject in Photos copies the subject and leaves the photo as it was. Tilora makes a new copy and leaves the original as it was.