To delete photos from one of your libraries, select them then either press command-delete or control-click the photos and select “Delete Photos” from the menu that appears. The photos will be deleted from the library, which will also remove them from any albums they belong to.
The photos are not deleted permanently when doing this though, but rather are moved to the “Recently Deleted” album in the library and will be automatically deleted by Photos after 30 days. If you wish to immediately delete the photos (e.g. to free up disk space), open the library in Photos, select the “Recently Deleted” album, then click the “Delete All” button in the upper right.
You can also “undelete” photos from the Recently Deleted album by selecting them and clicking the “Recovery” button. This will move the photos back into the main library, and add them back into any albums they belonged to before they were deleted.