Hardening off means to slowly acclimate the plants to an outdoor environment, after starting them indoors, or when moving house plants outdoors for the summer.
For seedlings, begin moving them outdoors about 2 to 3 weeks before you want to plant them in the ground. Place them in a shady place on the first day and bring them in at night. Each day, increase the length of time they spend outdoors. I take mine out 10 or 15 minutes earlier each day and bring them in 10 or 15 minutes later each evening, but there is nothing "magic" about the 10 to 15 minute time period. It's just what I came up with years ago, and it seems to work well for me. You may need to use a shorter time period, or be able to use a longer one, depending on the climate and weather patterns where you're located.
You also want to move your plants to a spot with a little bit brighter light every day or two. Unless there's a cold spell or heavy rain, you should be able to leave your seedlings out all day and all night, and in full sun if it's appropriate for the species, after about 2 to 3 weeks.
"Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too?" - Douglas Adams