For Cumulative Learning in artificial intelligence, see Multi-task learning
Cumulative learning is the cognitive process by which we accumulate knowledge and abilities that serve as building blocks for subsequent cognitive development. A very simple example is the saying 'you can't run before you can walk'; the procedural memory built while learning to walk is necessary before one can start to learn to run. Pronouncing words is impossible without first learning to pronounce the vowels and consonants that make them up (hence babies' babbling).
This is an essential cognitive capacity, allowing prior development to produce new foundations for further cognitive development. Cumulative learning consolidates the knowledge one has obtained through experiences, allowing it to be reproduced and exploited for subsequent learning situations through cumulative interaction between prior knowledge and new information.
Arguably, all learning is cumulative learning, as all learning depends on previous learning (except skills that are innate, such as breathing, swallowing, gripping etc).