Note my spelling and other corrections above. Usually, making the bed doesn't involve putting the mattress on - it's usually just putting on or straightening the sheets, pillow and covers.
Back before beds were permanent fixtures in houses and apartments, people would roll up their beds (which were made of straw) and put them next to the wall. Then in the evening they would "make their beds" and they would lie down and go to sleep. (Then the next day they would do it all over again.)
(I didn't realize when I asked that question how hard it would be to find an explanation on the Internet.)
Note my spelling and other corrections above. Usually, making the bed doesn't involve putting the mattress on - it's usually just putting on or straightening the sheets, pillow and covers.