Everybody involved in cryptocurrency needs a wallet to store their cryptos and for sending and receiving payments. For every wallet created for bitcoins and altcoins, there are private keys and public addresses attached to each of this wallet.
Public addresses are usually generated through complex mathematical function from private keys while private keys are created through complex cryptographic function also. Public addresses are like bank account numbers in the fiat world for sending and receiving payments and private keys allow owners of cryptocurrencies to access their funds. Without private keys, funds are lost. Private keys are responsible for preventing unauthorised access to funds and securing wallets against theft or hack.
Wallets which can either be hot wallets, mobile wallets, web wallets, paper wallets and cold storage wallets like trezor and ledger nano have private keys respectively for accessing funds.