Tesla is a unit of magnetic field. Another unit of magnetic field is a gauss. A refrigerator magnet is 100 gauss, a strong refrigerator magnet. The typical strength of the Earth's magnetic field at its surface is around a half a gauss. So those are everyday units of magnetic fields. There are 10,000 gauss in one tesla.
The magnets that we have here at the Magnet Lab range anywhere from 20 tesla all the way up to to 45 tesla for DC fields. In pulsed fields, they can go as high as 100 tesla, and even higher. So the magnets that we have at the Magnet Lab are much stronger than what you'd find in everyday life.
And it's even more impressive when you realize that the energy required to produce magnetic field goes like the square of the magnetic field. So to go from a 1 tesla to a 10 tesla magnet requires 100 times more energy.
Nikola Tesla was a scientist around the turn of the century, and the designation for magnetic field is named after him.