How does it work? "the latest algorithms being discovered at leading academic institutions" reads like marketing fluff to me.
The simplest explanation is pattern matching: we analyze customer and transactional data to understand how different customers behave. Using this understanding we can make predictions for how each user will behave in the future.
We use all of that analysis to power actions - take actions on the right user at the right time, optimizing for CLV.
Here's more: https://www.custora.com/home/customer_lifetime_value
The second is figuring out which promotions/emails go to which people. This is a supervised learning problem. We train the model with users past responses to discounts and their past behavioral states (which are the posterior probabilities from the latent attrition model). Then we use this to predict how users in those states will respond to similar promotions in the future.