Ability

You can see list of abilities that you aquire in this screen. By clicking button, you will see ability dialog like below:

From top to bottom, there are

Ability Name
Ability Type (Character or Job)
Description
Progress

Progress are the amount of TPs you need to level up selected abiities. Depends on ability its progress path are different - for example some of them only have one level but you need lot of TP, or you might have lots of levels with different TP requirement like shown above.
So here, in order for you to reach Battle LV2, you need to allocate 80 TP at Training Hall.

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