Because weather models are run in different parts of the world and also cover different parts of the world, a universal time concept is preferred.  Z-time refers to Zulu time and is also known as Greenwich Mean Time (GMT) based on time at the Zero Meridian longitude line.  Hour 0 is midnight GMT.  To calculate for the East Coast for example, one needs to subtract four hours during Daylight Savings Time (8pm is 0z) and five hours for standard time (7pm).  Models listed as a 0z or 12z run mean that is the time they were initialized.  It typically takes considerable time (especially for global models) for the actual output to arrive after the initialization time.  For example, the 12z GFS operational model (7am EDT initialization) starts arriving around 1130am EDT while the 12z European model starts to arrive by 1:45pm EDT.