'Partial performance' is less than complete performance and therefore gives rise to a breach of contract. It arises in circumstances where the performance is not close enough to complete performance to substantially give the non-defaulting party the intended benefit of the contract.
If the partial performance is a breach of condition, the non-defaulting party can reject the performance, put a stop to further performance of the contract and sue for damages. If the breach is a breach of warranty, performance cannot be rejected or terminated, but damages can be claimed.