Consider a direction $(\theta, \phi) = \hat{n}$, by fitting Planck's law to the radiation density you get the temperature $T(\hat{n})$. Define the quantity
$$
\delta(\hat{n}) = \frac{T(\hat{n}) - \bar{T}}{\bar{T}} = \frac{\Delta T(\hat{n})}{\bar{T}} \tag{1}\label{1}
$$
It is alway possible to expand Eq. $\ref{1}$ in spherical harmonics
$$
\delta(\hat{n}) = \sum_{lm}a_{lm}Y_{lm}(\theta,\phi) \tag{2}\label{2}
$$
If you think of $\delta$ as a random process, you can calculate things like the autocorrelation function of the temperature fluctuations
$$
C(\theta) = \langle \delta(\hat{n}_1) \delta(\hat{n}_2)\rangle, ~~~\mbox{with}~~~ \cos\theta = \langle \hat{n}_1| \hat{n}_2\rangle \tag{3}\label{3}
$$
It is not difficult to show that
$$
C(\theta) = \frac{1}{4\pi} \sum_l(2l + 1) C_l P_l(\cos \theta), ~~~\mbox{where}~~~ C_l = \langle |a_{lm}|^2\rangle \tag{4}\label{4}
$$
and $P_l$ the Legendre polynomial of degree $l$. Note Eq. $\ref{4}$ is just a link between $C_l$ and the autocorrelation of the random process $\delta$, as matter of fact the orthogonality of $P_l$ can be used to express $C_l$ as a function of $C(\theta)$.
The advantage of going this route is that in the linear regime $\delta$ is related with the mass perturbations $\Delta$, indeed
$$
\delta = \frac{1}{4}\Delta
$$
And there's a whole formalism to calculate $\Delta$ (See for instance Ch. 3 of this reference), for instance it is possible to show that for angular scales the density perturbations that give raise to the temperature fluctuations have a wavenumber $k \gg 2\pi a /ct_{\rm dec}$ ($t_{\rm dec}$ = time of decoupling), and
$$
C_l \sim \frac{1}{l(l + 1)}
$$
