This is the 60th most frequent Lithuanian word.
tuo
"That" or "with that" (instrumental case of "tas").
In this sentence, "tuo" is the instrumental case of "tas" (that), used to indicate the means or tool with which the action is performed.
Aš naudoju tuo galąstuvu, kad pagaląsčiau peilį.
I use that sharpener to sharpen the knife.
Here, "tuo" functions as an instrumental case form of "tas," meaning "that," to emphasize a comparative degree.
Jeigu darysi kaip Aistė, būsi tuo geresnis.
If you act like Aistė, you will be all the better.
In this instance, "tuo" forms a temporal phrase "tuo metu," meaning "at that time." It serves to reference a specific point in time.