A fileless infection (fileless malware) is malicious coding that exists only in memory rather than installed to the target computer's hard drive.
Fileless malware is written directly to RAM. The code is injected into some running process, such as iexplore.exe or javaw.exe, which is then used for the exploit. Users typically contract fileless malware by visiting a malicious website, which they may be redirected to after clicking the attacker's ad (malvertisement). Because the malware doesn't exist as a file, it can often elude intrusion prevention systems and antivirus programs.
The infection cannot persist through a reboot because RAM, as volatile memory, only holds its data while the system is powered up. However, while the infection is live, the attackers may be able to steal data or download more persistent malware.
See an introduction to fileless malware: