Maybe you’re wondering why baking dirt is a useful thing. Wonder no longer.
Every element in the periodic table has its own atomic mass. Some bright spark thought that it should be possible to make use of this uniqueness to be able to identify what elements are in any unknown clump of “stuff”. That bright spark came up with a mass spectrometer to do this. The spectrometer takes atoms of “stuff”, gives them a little positive or negative charge (ionizes them), and then shoots them through a controlled electromagnetic field. That field will exert forces on the charged atoms and cause them to deflect from the path they’ve been shot on. Particles of greater mass will deflect less than ones with less mass in the same field. By measuring that deflection and knowing all the other variables (the amount of charge you’ve applied, the strength of field you’ve created, etc.) you can determine the masses of the atoms. And because they have unique masses, you can match that up to the periodic table and know what’s in your “stuff”.
To get your individual atoms and be able to ionize them you need to be able to make them into a gas. That means baking them, heating the “stuff” up until some of it, at least, starts to vaporise. Then you do your mass spectroscopy, and bob’s your uncle.
This is what the TEGA on Phoenix is. It’s a high-temeprature oven to vaporise the dirt, and a mass spectrometer to determine what elements are in the dirt. It’s so sensitive, in fact, that it can differentiate isotopes of the same element. That’s important, because information about the ratios of different hydrogen, oxygen, carbon, and nitrogen isotopes might provide info about whether conditions on Mars have ever been suitable for some type of life. Now that TEGA’s finally got a big lump of dirt in it they can start doing that.