u.c. - una corda - from the Italian: one string (press the left pedal)
t.c. - tre corda - from the Italian : three strings (stop depressing the left pedal and go back to normal playing).
On a grand piano the left pedal shifts the hammers to the right, so that instead of the hammer striking all three strings at the same time, it strikes only one string (hence una corda). So you have the same volume, but a more transparent sound (not so rich in enharmonics).
On an upright piano however you will not have this effect, since the left pedal brings the hammers close to the strings (rather than laterally displacing them), and therefore if you press the left pedal all you get is a lower volume.
Best wishes,
Bernhard.