Johnny Novgorod said:
I've never played it but from what I've heard it sounds kinda like Demon's Souls in the sense that you don't achieve anything except activate shortcuts through worlds that otherwise remain unchanged (I don't know how this works with boss fights, if there are any).
Kind of true. Any shortcuts that may be activated are usually inactive when the days cycle back to the first day. However, you do get a song that lets you fly to any save point that you have activated. This is what is generally used to bypass a lot of the work the second time through an area. Of course, songs in general let you go to areas you otherwise couldn't have, as there are several that you need to do a lot of work to obtain; these let you access the dungeon area generally, which was closed off, or otherwise inaccessible.
As for bosses, if you defeat a boss, then you can warp straight back to them a stone plaque located in the dungeon's entrance. This of course makes things much easier if you are going after a specific goal that requires the boss to die after a second time through the area. Most notabley, beating the Snow Head Temple's boss and/or the Swamp Palace's boss will have a effect on the surrounding landscape outside of their respective dungeons. This will let you access events otherwise not possible to start or complete. Of course, you can always go back to boss with new gear and see how you fare as well.
You definitely have an impact on the world, but at Yatzee says, it is generally contributed to the masked form you took(which is generally a well known person of that area). Of course, this all gets erased when you turn back time, but you can always do it again if you so choose.