You are right, nbits is current network difficulty.
Difficulty encoding is throughly described here.
Hexadecimal representation like 0x1b3cc366 consists of two parts:
- 0x1b -- number of bytes in a target
- 0x3cc366 -- target prefix
This means that valid hash should be less than 0x3cc366000000000000000000000000000000000000000000000000 (it is exactly 0x1b = 27 bytes long).
Floating point representation of difficulty shows how much current target is harder than the one used in the genesis block.
Satoshi decided to use 0x1d00ffff as a difficulty for the genesis block, so the target was0x00ffff0000000000000000000000000000000000000000000000000000.
And 1078.52975077 is how much current target is greater than the initial one:
$ echo 'ibase=16;FFFF0000000000000000000000000000000000000000000000000000 / 3CC366000000000000000000000000000000000000000000000000' | bc -l