Hardening is the process of prepping a plant that's been started indoors for life outdoors, specifically against sunlight.
The brushing I mentioned to thicken the stems up as the grow is also hardening, only against rain and wind.
For sun, what you do is carefully, over a period of a week or two, expose the plants to longer and longer periods of sunlight. So say, start out putting them in early morning or late afternoon sun for an hour, and slowly increase that each day, and move it more into mid day sun. By the end your plants should be able to withstand a full day of sun.
If you don't do this, most likely plants that have lived fairly sheltered indoor lives to that point, will whither and die if you just move them from indoors to out with no hardening. They just haven't enough protection against it.
Think of it sort of like giving your plants a tan so they don't burn when they go out for real.