BIP-32 describes what Hierarchical Deterministic wallets (HD wallets) are and how they operate. An HD wallet is a system for deriving seemingly infinite private/public key pairs from a single point referred to as a seed. This creates a hierarchical tree-like structure of private/public keys.
From a mnemonic phrase (see BIP-39) a seed is derived. That is hashed and a master key, also known as a parent key, is derived. From that parent key, you can then derive child keys underneath that. From each of the children you can derive more child keys. Think of it as a tree branching out. This structure allows the owner of the wallet to provide one of the branches, or sub-trees, to someone else and they can then generate more addresses further down that tree.
Deterministic wallets eliminate the need for a user to document every single private/public key because they can be regenerated at anytime with the single mnemonic phrase that's held by the wallet owner.