Wiktionary
n. (context computing English) A set of software tools used by a third party after gaining access to a computer system in order to conceal the altering of files, or processes being executed by the third party without the user's knowledge. vb. (context transitive English) To infect (a computer system) with a rootkit.
Wikipedia
A rootkit is a collection of computer software, typically malicious, designed to enable access to a computer or areas of its software that would not otherwise be allowed (for example, to an unauthorized user) while at the same time masking its existence or the existence of other software. The term rootkit is a concatenation of "root" (the traditional name of the privileged account on Unix-like operating systems) and the word "kit" (which refers to the software components that implement the tool). The term "rootkit" has negative connotations through its association with malware.
Rootkit installation can be automated, or an attacker can install it once they've obtained root or Administrator access. Obtaining this access is a result of direct attack on a system (i.e.), exploiting a known vulnerability (such as privilege escalation) or a password (obtained by cracking or social engineering). Once installed, it becomes possible to hide the intrusion as well as to maintain privileged access. The key is the root or administrator access. Full control over a system means that existing software can be modified, including software that might otherwise be used to detect or circumvent it.
Rootkit detection is difficult because a rootkit may be able to subvert the software that is intended to find it. Detection methods include using an alternative and trusted operating system, behavioral-based methods, signature scanning, difference scanning, and memory dump analysis. Removal can be complicated or practically impossible, especially in cases where the rootkit resides in the kernel; reinstallation of the operating system may be the only available solution to the problem. When dealing with firmware rootkits, removal may require hardware replacement, or specialized equipment.