You've picked a seriously tricky bit of music to use to learn score reading. But to attempt to clear up your problem with the arcs....first of all the things you're looking at are ties (not slurs or phrase marks which have a completely different purpose). Ties connect a number of written notes of the same pitch and you play only one note. The length you play is the lengths of all the written notes added together.
As for why ties are used it's all down to the sometimes odd rules of music writing, There are two main reasons:
1. You aren't allowed to write a note which would play across a bar line e.g. in 4/4 you can't write a note 6 beats long...so if you need one you have to write the note separately in each bar and then tie them together.
2. If you want a note that lasts for a non-standard length of time like 3 7/8 beats there's no way to write that note length in one go so you have to write several smaller notes and tie them together to make up the correct note time.
From what I can see the bit you're looking at uses both reasons, it's a very long note across several bars AND it's an odd length.
Hope that didn't confuse you still more.
Steve
As for why ties are used it's all down to the sometimes odd rules of music writing, There are two main reasons:
1. You aren't allowed to write a note which would play across a bar line e.g. in 4/4 you can't write a note 6 beats long...so if you need one you have to write the note separately in each bar and then tie them together.
2. If you want a note that lasts for a non-standard length of time like 3 7/8 beats there's no way to write that note length in one go so you have to write several smaller notes and tie them together to make up the correct note time.
From what I can see the bit you're looking at uses both reasons, it's a very long note across several bars AND it's an odd length.
Hope that didn't confuse you still more.
Steve