I'm a little worried about what might happen when the three days (72h) are over. It took me a long time to play this hide and seek game and now it's already the night of the second day. What will happen if those three days are over and there is still a mission you need to do? Do you have to do it all over again? I don't hope so though.
On the Final Day, you'll find out what happens after your 72 hours are over. Given how early you are in the game, it's a bit spoiler-y. I'd recommend that you just play through to the Final Day and you'll see what happens after the three days are over. If you can't wait, the next bit is in spoiler text (just mouseover to reveal).
On the Final Day, the Clock Tower will open up. If you have access to the Town Deku's flower (through trading him the Moon Tear), you can fly up to the Clock Tower entrance and run up to face the Skull Kid. After a cutscene, you'll need to re-acquire your ocarina and you will prompted to play the Song of Time. This will rewind the timeline 3 days and thus the major mechanic of Majora's Mask will be revealed. You'll be constantly rewinding time throughout the game, losing most items and resetting progress with the exception of your masks, Heart Pieces, and key items like your Bow or your ocarina.
If you're asking about what happens you aren't prepared at the end of your first Final Day, I hope it's not very spoilery to say
rocks the Moon falls and everyone dies you get brought back to the Dawn of the First Day.
The ultimate goal of the first three days is to gain access to the Clock Tower, to
"...get back the precious item that was stolen from you."
However, if you are unable to get there in time, the time you were given, will reset, similar to the control you are given later in the game. But without first accessing the clock tower, you will be unable to progress into the main story of the game.
The good thing about this is that if you write down codes (i.e. the "Bomber's" code to their hideout), you won't need to re-do that part of the game, and thus save time.