If you drive to work in the morning, you probably do so in a gasoline-powered car. Compared against the electric cars that actually exist (versus maybe the ones we wish existed), gas-powered cars just make more sense for most people: they're just much cheaper and far more convenient than electric.
But what if we could go back in time, and start again so that history went down a different path? Maybe if electric cars had caught on in the beginning then, a hundred years later, all of the research and investment that has now gone into gasoline-powered cars would have gone into electric cars instead. And so maybe if we'd gone down that other path we'd now be living in a world where electric cars were cheaper and more convenient, and gasoline powered cars (if they existed, perhaps for some special uses) would be more expensive and less convenient.
Why did gasoline cars catch on in the first place, then? Well, it could be that they were introduced first and just had more time to become popular before electric cars had a chance. Maybe gas was really cheap at the time (because there weren't a lot of cars on the road) and by the time gas prices climbed we'd already built all the infrastructure for gas. Maybe it was just weird, random luck – maybe things don't always happen for a good reason, even a reason that makes sense at the time. (If you're interested in cars specifically you can read more about the history of electric cars at Wikipedia, but each of the reasons described here could be a plausible reason why path dependence happens).
The thing that each of these stories share is an idea lock in. Once we live in a world where everyone else has a gasoline car, and all the infrastructure is based around gasoline cars, and 100 years of research and development and investment has gone into optimising gasoline cars, we might all find that it's in our interests (individually) to buy gas-powered cars. But it might still be that – down the other path, if history had worked out differently – we might now be living in a world where electric cars were dominated, and it might well be that that world would be a "better" world in various ways we care about.
There are lots of other situations where lock-in just doesn't apply. For example, in the 70s people wore lots of bell-bottomed jeans. But there was no real lock-in to bell-bottomed jeans versus straight jeans, and if people now want to wear straight jeans instead there's nothing stopping clothing companies from making lots of straight jeans and nothing stopping consumers from buying those straight jeans.
People use "path dependence" to mean a number of different things, unfortunately. But this, to me, is the most useful version: the idea that, in theory, lock-in can cause us to wish that the world had gone down a different path instead; where each of us individually is better off doing a certain thing (buying gasoline cars, for example) even though in that alternative universe we'd be better off buying electric cars, and that alternative universe would be "better" overall. Some people are very skeptical that path dependence ever actually happens in the real world (and fair enough: if your favoured technology doesn't catch on, it might be easier to argue "oh, it's path dependence, the world is screwing up here" than to admit "other people just don't value this technology as much as I do, perhaps for valid reasons"). Peronally I don't know; I think the concept is useful, but I don't know enough about any of the famously-used examples to say for sure what happened with them.
You might have noticed a little electric car company called Tesla making waves recently; they seem pretty set on converting the world to electric cars, and maybe they'll succeed. And people on both sides can use this to argue their case. If Tesla succeeds, maybe that's proof that Path Dependence doesn't really happen in the real world (on a meaningful scale): that once the benefits of switching become high enough, someone will find a way to displace the old technology and take us down a different path. But to the other side, maybe that's proof that we were stuck on the wrong path for a really long time and could have been in a better world a long time ago if it weren't for path dependence problems.