Keeping a record of contacts is important in amateur radio. While not required by the FCC in the United States, logging is definitely encouraged.
For the common, everyday VHF/UHF radio chatter we participate in on a local repeater, contacts are rarely logged. This is fine, since logging of these would be a tedious nuisance. Logging of all other contacts is highly recommended.
Besides frequency, call sign and signal report, date and time of contact are logged. Time should be when contact begins, not when completed.
In practice, active hams live in two time zones. The first is their local time, which is when they join a net or sign off a contact because dinner is being served.
Local time is what should be recorded in emergency communication (EmComm) logs when participating in drills or actual disaster deployments where local time is more meaningful.
The second zone hams more frequently use for logging is Zulu time, the current time at the Prime Meridian of the World running through Greenwich, England. Zulu time (Z) is also known as Greenwich Mean Time (GMT) or Coordinated Universal Time (UTC or sometimes UCT). If it’s coordinated Universal Time, why is it Called UTC and not CUT?
Technically GMT is a time zone while UTC is a time standard (details) but practically speaking they are the same thing and in the aviation, military and telecommunications world it’s Zulu time.
Why the name Zulu? There are 25 integer World Time Zones from -12 through 0 (GMT) to +12. Each one is 15° of Longitude as measured East and West from the Prime Meridian. These are given alphabetic designations A-Z, less the letter J. Z (ITU phonetic Zulu) corresponds to the prime meridian at 0° longitude. Zulu time.
When logging all but EmComm contacts, hams should use Zulu, not their local time. Then both parties in a logged contact have the same (universal) time and date recorded (date will change at midnight between 2359z and 0000z). This becomes important when confirming contacts and getting awards.