Store TP is an ability that accelerates TP gain.
The exact mechanics are a well-guarded secret of the developers, but this ability in action functions approximately as follows. If a Ninja were to hit an enemy with a Great Katana, he would accumulate about 11% TP per hit. If a Samurai hits with a Great Katana, depending on his level, he will gain 12-13%TP. This works for all weapons, but it seems that the Great Katana is the weapon most effected by the Store TP ability.
There are wearable items with a Store TP effect. Most are for Samurai, but not all.
For example, the Shinimusha Hara-ate has Store TP+9. Store TP+9 does not actually translate into +9% TP per hit. In fact it seems that the number that is added to the Store TP ability is in tenths of a percent so "Store TP+9" actually would add about .9% TP per hit. This might not seem like much, but it does help accumulate TP quickly. TP is not only gained by hitting a creature, but also every time a player is hit by a creature, a spell, or an area-of-effect ability. Store TP affects the gained TP from all sources.
Store TP is a Lancer ability that raises TP gain by 5%. Some gear pieces and materia also provide the Store TP ability.