The phrase "to sterilize the jars" means to make the jars completely clean and free from any bacteria or germs that might spoil the food inside. Full definition
After one minute take off the heat and ladle into sterilized jars half pint or pint size jars leaving 1/4 in head space. (you-made-that.com)
To do that, they soaked fruit fly eggs briefly in bleach, washed them in alcohol, and grew them in sterilized jars with sterilized food — treatments that prevented the flies from picking up the menagerie of bacteria that usually climb aboard early in life. (sciencemag.org)
Then take the left over grains and place in a new clean, sterilized jar with new fresh milk. (nutritiousndelicious.com)