A few days before tomato plants go into the garden, they should be put outside to get accustomed to the conditions. This is called hardening off, as the plants need to get hardened to the weather.
I'm lucky that I have a screened-in porch that gets some sun in the morning only. Like humans, tomato plants will get sunburn if they are exposed to too much sun right away. They need a little sun at a time, to get used to it.
The clear storage boxes are a good way to move plants inside or outside in a group, and the height of the boxes protect the seedlings from breezes. You don't want the poor plants to be thrown about in the wind!
When the low temperature for the night is supposed to be 45 or above, I leave the plants outside all night. What doesn't kill them makes them stronger, right? If it's supposed to be fairly windy, I bring them inside.
If you don't have plastic storage boxes to protect your plants, they say to put your plants outside in a sheltered spot. I guess they mean sheltered from too much sun, wind, and pets or varmints. After 10 days of hardening off, your tomato plants should be ready for prime time in your garden!