Bitcoin is often described as an anonymous currency because it is possible to send and receive bitcoins without giving any personally identifying information. However, achieving reasonable anonymity with Bitcoin can be quite complicated and perfect anonymity may be impossible.
Bitcoin is pseudonymous. Sending and receiving bitcoins is like writing under a pseudonym. If an authors pseudonym is ever linked to their identity, everything they ever wrote under that pseudonym will now be linked to them. In Bitcoin, your pseudonym is the address to which you receive Bitcoin. Every transaction involving that address is stored forever in the blockchain. If your address is ever linked to your identity, every transaction will be linked to you.
In the original Satoshi whitepaper, it was recommended that Bitcoin users use a new address for each transaction to avoid the transactions being linked to a common owner. This would be the equivalent of writing many books under different pseudonyms. Although this remains a best practice, it is not enough to guarantee full anonymity due to multi-input transactions.