If you look at this gif image (least significant byte LSB values for the blocks mined 2009 - mid 2010)
What exactly is this chart showing that the addresses/keys could be in a set range?
No. This has nothing to do with addresses at all.
When mining a block, the miner adds a
4-byte value called a "nonce" to the block header before hashing it. This allows them to quickly change the block header (by changing the nonce) without needing to change which transactions they've included in the block or the order of those transactions. As such, they are able to compute LOTS of hashes VERY quickly:
- Step 1: Build block
- Step 2: Add nonce to header
- Step 3: Hash header
- Step 4: Is hash value lower than difficulty target?
- Step 5: If yes, block is "solved", broadcast block. Otherwise continue.
- Step 6: Block is NOT solved. Have ALL possible nonce values been tried yet?
- Step 7: If not, increment nonce, go back to Step 3. Otherwise continue
- Step 8: Block is not solved, all nonce values attempted. Build a new block.
- Step 9: Goto Step 2
A byte value can be represented in hexadecimal with 2 characters and is typically written in documentation with a 0x in front of it to indicate to the reader that the value is a hex value and not a base 10 integer value:
Hex value = base 10 integer value
0x00 = 0
0x01 = 1
0x02 = 2
0x03 = 3
...
0x09 = 9
0x0A = 10
0x0B = 11
0x0C = 12
0x0D = 13
0x0E = 14
0x0F = 15
0x10 = 16
0x11 = 17
and so on.
When you have a 4 byte integer the LSB (least significant byte) is the byte that changes the fastest as you count up (think of the digit on the far right side of the way you usually right numbers).
The graph that was posted is the quantity of blocks that have that particular value in the LSB between the genesis block and the block number indicated.
So, when the graph looked like this:

It is indicating, for example that there were approximately 70 blocks between block height 23400 and 26400 that had a nonce with a base 10 integer value of 20 (0x14).
The vertical axis is the quantity of blocks matching the condition.
The horizontal axis is the base 10 integer value of the LSB.
The title at the top of the graph is the block range that the data represents.