A zero-day attack is an attack that is still unknown to the vendor, software developer, and/or system administrators. It is an attack that is newly discovered by malicious users.
A zero-day (also known as a 0-day) is a computer-software vulnerability previously unknown to those who should be interested in its mitigation, like the vendor of the target software. Until the vulnerability is mitigated, hackers can exploit it to adversely affect programs, data, additional computers or a network. An exploit taking advantage of a zero-day is called a zero-day exploit, or zero-day attack.
The term "zero-day" originally referred to the number of days since a new piece of software was released to the public, so "zero-day software" was obtained by hacking into a developer's computer before release. Eventually the term was applied to the vulnerabilities that allowed this hacking, and to the number of days that the vendor has had to fix them. Once the vendors learn of the vulnerability, they will usually create patches or advise workarounds to mitigate it.
The more recently that the vendor has become aware of the vulnerability, the more likely it is that no fix or mitigation has been developed. Once a fix is developed, the chance of the exploit succeeding decreases as more users apply the fix over time. For zero-day exploits, unless the vulnerability is inadvertently fixed, such as by an unrelated update that happens to fix the vulnerability, the probability that a user has applied a vendor-supplied patch that fixes the problem is zero, so the exploit would remain available. Zero-day attacks are a severe threat.