The formula you quote seems to be just the law of total probability. Assume that the set of events $\{ H_\eta \}_{1 \leq \eta \leq \mathbb H}$ forms a partition of the sample space $\Omega$; i.e., the $H_\eta$'s are pairwise disjoint, and $\bigcup \limits_{\eta = 1}^{\mathbb H} H_\eta = \Omega$.
Now for any event $E_e$, the set of events $\{ E_e \cap H_\eta \}$ forms a partition of $E_e$. Therefore, by additivity, we have $ P(E_e) = \sum_{\eta = 1}^{\mathbb H} P(E_e \cap H_\eta). \tag{1} $ Now, by the definition of conditional probability, we have $P(E_e \cap H_\eta) = P(H_\eta) \cdot P(E_e \mid H_\eta)$. Plugging this in $(1)$ we get the claim.*
The following sentence taken from the wikipedia article explains what this theorem means intuitively (notation changed to match ours):
The summation can be interpreted as a weighted average, and consequently the marginal probability, $P(E_e)$, is sometimes called "average probability"; "overall probability" is sometimes used in less formal writings.
*The formula is true even for $\{ H_\eta \}_{\eta \geq 1}$ forms a countably infinite partition of $\Omega$. The proof has to be modified only slightly for this.