So what does
00000000 00000F61 B1000000 00000000 00000000 00000000 00000000 00000000
How does that relate to difficulty 1090715.6800513?
The large number is the TARGET. For a hash to be valid (and solve a block) it must be smaller than the target. They are just two ways of expressing the same thing.
DIFFICULTY is somewhat arbitrary but easier for us humans to comprehend. The first block had a target of:
0x00000000FFFF0000000000000000000000000000000000000000000000000000 = difficulty 1
0x0000000000000F61B10000000000000000000000000000000000000000000000 ~= difficulty 1.09 million
The starting difficulty (diff 1) will occur roughly once per 2^32 hashes so that is where the concept of a share comes into play.
With difficulty of 1 you will solve on average 1 block every 2^32 hashes or 1 share.
With difficulty of 1090715.6800513 you will solve on average 1 block every (1090715.6800513)*(2^32) hashes or 1090715.6800513 shares.
Hopefully that didn't leave you more confused.
TARGET = what we need the hash to be under.
DIFFICULTY = shorthand. When we say difficulty 1 million we mean the target is 1 million times smaller.
As difficulty rises the target gets smaller.