This message is directly coming from bitcoin.org to raise awareness of a potential state sponsored attack and about possible mitigation:
Bitcoin.org has reason to suspect that the binaries for the upcoming Bitcoin Core release will likely be targeted by state sponsored attackers. As a website, Bitcoin.org does not have the necessary technical resources to guarantee that we can defend ourselves from attackers of this calibre. We ask the Bitcoin community, and in particular the Chinese Bitcoin community to be extra vigilant when downloading binaries from our website.
In such a situation, not being careful before you download binaries could cause you to lose all your coins. This malicious software might also cause your computer to participate in attacks against the Bitcoin network. We believe Chinese services such as pools and exchanges are most at risk here due to the origin of the attackers.
The hashes of Bitcoin Core binaries are cryptographically signed with this key.
We strongly recommend that you download that key, which should have a fingerprint of 01EA5486DE18A882D4C2684590C8019E36C2E964. You should securely verify the signature and hashes before running any Bitcoin Core binaries. This is the safest and most secure way of being confident that the binaries you’re running are the same ones created by the Core Developers.
If you don’t how to verify the integrity of a file, head over the instructions page of openoffice.org. There you will find explanations available for Windows, Linux, online and more: