'Hardening off' means to acclimatise your punnet of seedlings before being planted into the garden.
As simple as it sounds, many gardeners do not know how to do it and end up losing their new plants soon after planting out.
If you have sown your plants from seed and kept them indoors until they are well developed they will be 'soft' and will die quickly if planted out from being in such comfortable conditions. Likewise if you have bought your plants from a hardware store and put off planting for a few days.
Rule of Thumb
Give the seedling punnet the same amount of days outside as you had it inside the house.
So if you bought your plants four days ago and kept them on the windowsill, then you need to give them four days outside under the porch or veranda for the first day, then gradually moving the punnet into the sun before finally planting them into the garden on the fifth day.
If moving your plants from a greenhouse, the best time in on cooler, overcast days. Overcast conditions keep the stress of the plant to a minimum.
Do not expose the seedlings to intense heat or a night of frost during the hardening off period.
Your plants will then be ready to handle the outside temperatures.
To boost your plant's ability to cope with the transplanting, frost, resist diseases and establish a healthy root system, apply a little seaweed solution at the time of planting (e.g. Seasol).
If you are at all worried about how your new seedlings will cope, try adding a few seeds of the same plant amongst the seedlings at the same time as planting out as a back up measure.