It's a long sword used by the samurai of medieval Japan, it is worn slung under the belt with the edge pointing down and designed to be used on horseback. It's very similar to the katana, however to usual things that distinguish it are:
- How it's worn, instead of being held in by the obi (sash) it is slung on it using a loop on the saya (scabbard, sheath), also unlike the katana it is worn with the edge pointing down instead of up.
- The blades are usually more curved than the katana, as well as the hilt or handle of the sword to aid in drawing and help accommodate and balance the sword for mounted fighting on horseback.
- Sometimes the blades are also slightly longer (to reach the enemy from the horse) and made lighter (to be easier to balance in one hand) as well.
Overall the Tachi was in the end replaced by the katana during the Edo period due to the less prevalent occurrences of mounted warfare that was more common in the warring states periods. The katana became more practical due to the lack of warfare and became the more widely used weapon of the time.
If you want a better answer, I suggest reading up on the history of the samurai and their weapons.