A contest runs in one of two participation modes. In online mode everyone starts and finishes together, on the contest's own schedule. In virtual mode the schedule is a window, and each participant has their own clock that starts when they press Start.
The mode is chosen when you create the contest. Afterwards it is the Virtual toggle on Settings → General: off is online, on is virtual. It is locked once the contest is finalized.
The start time and the end time are the contest. Every participant works in that window, sees the same countdown, and stops when it runs out. This is the shape of a live event — a national round, an ICPC-style regional, a school olympiad — and it is what you want whenever fairness depends on everybody seeing the problems at the same moment.
The only thing you have to set is the schedule; there is no duration, because the duration is the window.
The start and end times bound a period, and Duration is how long a single participant gets inside it. A contest can run from midnight to 23:59 with a duration of four hours: a participant may begin at any point in the day, and then has four hours or until the contest's end time, whichever comes first.
Until a participant presses Start they see the contest page and a Start button, not the problems. From the moment they press it, their own window is open and their countdown runs.
This suits training rounds, qualification rounds and anything spread across time zones, where people cannot all be at a keyboard at the same hour.
The mode changes what the scoreboard can show. A virtual contest offers a Virtual board, where each participant is placed on their own clock; sorting, first-to-solve marks and the second rank column are not computed there, and that board cannot be sorted or exported.
It also changes what the roster looks like while the contest runs: in a virtual contest, participants sit at Ready until they choose to begin, so the statuses on the Participants tab are spread out instead of moving together.
Neither mode is the whole story of who may work on the problems and when. Two settings extend a contest past its end time, and both are described in Start time, duration and extra time:
Allow follow up lets someone who never took part join afterwards and work through the contest virtually and unofficially — an online contest that keeps giving people a way to sit it.
Allow upsolve lets people who did take part keep solving once their own time is over, with those results kept apart from the contest-time score.
They are different things: follow-up participation is a fresh, timed attempt at the contest, while upsolving is the original participant carrying on with no clock.