Premeditation is when you plan something ahead of time. A car thief's premeditation might include following a driver and noting where he typically parks his Mercedes.
You're most likely to see the noun premeditation when someone's talking about crime. Almost any kind of crime or wrongdoing is considered worse, especially in a courtroom, if there's premeditation involved. An assault that's spontaneous isn't punished as harshly as one that involves premeditation, in which the attacker plans the assault before carrying it out. The Latin root, praemeditationem, combines prae, "before," and meditari, "to consider."