For the Posion Distribution - what does "events occur singly in space or time mean"

Does it mean liek one at a time?

it means when you say 10 accidents per month

you may start the month at any point, but once you start the 30 days must run as a continuous interval
i.e no 3 days then a gap, then another 15 days then a gap and then another 12 days

similarly with length, area, volume (space)