Bitcoin right now is not really anonymous. While Bitcoin addresses aren't necessarily linked to real-world identities, they can be. Monitoring the unencrypted peer-to-peer network, analysis of the public blockchain, and Know Your Customer (KYC) policy or Anti-Money Laundering (AML) regulation can reveal a lot about who's using Bitcoin, and for what.
This is not great from a privacy perspective. Bitcoin users might not necessarily want the world to know where they spend their money, what they earn or how much they own, while businesses may not want to leak transaction details to competitors – to name some examples.
Additionally, bitcoins being traceable, possibly “tainted,” and potentially worth less than other bitcoins is at odds with fungibility. This could even challenge Bitcoin's value proposition as money.
But there are potential solutions to increase privacy, and improve fungibility.
One of these solutions is BIP 151, a Bitcoin Improvement Proposal designed to encrypt data among Bitcoin nodes.
https://bitcoinmagazine.com/articles/bip-the-end-to-end-encryption-bitcoin-never-had-but-soon-will-1465401187