There is very little intuition in there. Just some math. Consider the definition of g(2), which roughly translates into a constant and the photon number variation divided by the squared mean. For thermal light these two are pretty much equal, so you will get a value of two.
To be exact:
[itex]g^{(2)}(0)=\frac{\langle : n^2: \rangle}{\langle n \rangle^2}[/itex]
The double stops denote normal ordering which ensures that the detection of the first photon reduces the photon number by 1. That leaves you with:
[itex]g^{(2)}(0)=\frac{\langle n (n-1) \rangle}{\langle n \rangle^2}[/itex]
Of course you can represent the instantaneous photon number n as the sum of the mean [itex]\langle n \rangle[/itex] and some fluctuation [itex]\delta[/itex] about the mean. So you get:
[itex]g^{(2)}(0)=\frac{\langle (\langle n \rangle +\delta) (\langle n \rangle+\delta-1) \rangle}{\langle n \rangle^2}[/itex]
All terms linear in [itex]\delta[/itex] must of course vanish when taking the expectation value, so you are left with:
[itex]g^{(2)}(0)=\frac{\langle n^2 \rangle - \langle n \rangle + \delta^2}{\langle n \rangle^2}=1-\frac{1}{\langle n \rangle}+\frac{\delta^2}{\langle n \rangle^2}[/itex]
The [itex]\delta^2[/itex] term is proportional to the photon number variance. For thermal light, this is [itex]\langle n \rangle^2 +\langle n \rangle[/itex], which just leaves you with two.