Airlines overbook almost every flight. That means if you're not in that line, you have a good chance of getting booted off the flight. It has happened to me a couple times.
They normally give you a voucher to compensate you for the trouble that can be used on a future flight. They will typically try to rebook you (at no cost) the same day if they can arrange it.
Actually this happened to me this summer, came to board the flight and there weren't any seat left, so they told me to go to the gate in case somebody didn't show up.
I was lucky enough to board the plane, but yeah, overbooking is a thing in Europe
Yes it is, but a passenger has so many consumer rights that it can end up more expensive for airlines to overbook than it is to lose a fare or two. It's very rare for it to happen, and it's usually US airlines that do it in the EU because their US passengers don't know their rights in the EU
They will usually announce that they are overbooked and ask over the local section intercom if anyone is willing to take the next flight. You can actually get cash out of it if nobody else wants to go later, sometimes more than you paid for your ticket. Plus a free ticket for the next flight.
If you're not lined up (or late) and the plane is already full, then they can't seat you and you'll have to take a later flight by default.