A public address is covered in full under wallet address, which explains formats, checksums and how addresses are generated on different networks. This page explains the phrase itself, which is common in exchange interfaces and wallet guides.
A public address is the string of letters and numbers a person shares so that others can send them cryptocurrency, much like an account number given out for incoming transfers. It is normally derived from a public key, which is in turn derived from a private key. The word "public" stresses that the address can be shown to anyone without risk to the funds: only the private key can authorise spending. On a public blockchain every transaction to and from the address is visible, which is why addresses are described as pseudonymous rather than private.
The same idea goes by several names. Bitcoin users often say "receiving address", Ethereum users say "account" or "address", and many apps simply say "deposit address". Some wallets create a new address for each payment to make tracking harder, a practice supported by a hierarchical deterministic wallet. Sending funds to a mistyped address or to an address on the wrong network can mean permanent loss, and scammers exploit this with address poisoning, so users are advised to check every character before sending.