As the name suggests 3T means 3 tomoe sharingan, which basically represents that in three tomoe, you have third tomoe in the eye of sharingan, giving you more advanced abilities. Sharingan is the dojutsu and KG of Uchiha clan and hence pretty unique ability to have in itself.
3 tomoe sharingan grants you some unique abilities, they are as follows:
1. Ability to see chakra color: Very basic ability, using which you can also predict if you are in genjutsu or not. Although Byakugan is more detailed when it comes to chakra, as you can even see tenketsus using it. Something not possible using sharingan.
2. Visual perception: Sharingan gives you ability to differentiate between normal clones. Also, it gives you ability to see through a genjutsu, but doesn't give you ability to see through denser object or doesn't give you ability to see at objects present at long distance, something that is true in case of byakugan.
3. Sharingan genjutsus: Sharingan gives you access to unique genjutsus, which are sharingan genjutsus. One can cast genjutsu on his opponent using simple eye contact, which is very big advantage of sharingan. You can even take complete control of person's body, which also worked on tailed beasts in manga.
4. Predicting opponents' moves: Sharingan can be used to closely follow the movement of your opponent as your opponent looks as if he is moving in slow motion. You can the mimic his movements so as to make it appear that you are 'seeing future'. Also, you can closely watch the handseals and accordingly predict the upcoming ninjutsu move or copy the handseals to perform the same move against opponent.
5. Genjutsu resistance: Using 3T sharingan, one can easily break out of B-Rank visual genjutsu. Also, there is a technique called as heaven and earth exchange(citation needed), which can be used to take control of opponent's genjutsu and reverse it on him/her. This makes sharingan masters pretty good with genjutsus and hence difficult to beat in genjutsu battles.
Now, about the difference between 3T and others, I must say 3T makes you better in abilities 1,2 and 4, while abilities 3 and 5 are specific to 3 tomoe sharingan only. This is the reason having 3 tomoe is an honorable ability.
It was unusual for Sasuke to talk that much. He wasn't used to it and hence needed to drink some water, before he can proceed with his training.