In 1945 the allied forces dropped two nuclear warheads on the Japanese cities of Hiroshima and Nagasaki. Today, both cities are not only rebuilt but populated. By contrast, the Chernobyl accident which occured in 1985 led to an exclusion zone which is still heavily patrolled; Chernobyl is still radioactive while Hiroshima and Nagasake are not. How come?
What's really worth mentioning here is that nobody actually has a clue what happens to the world in long term after a nuclear event. Because it doesn't happen very often, all the claims you hear about "this place will stay radioactive for 40,000 years" are really just hypotheses because nobody is 100% sure. But here's what we do know.
When Little Boy (the Hiroshima bomb) detonated, around 0.9 kilograms of nuclear fuel was actually activated, enough to destroy a city but not a huge amount of actual stuff. By contrast, Chernobyl was not a nuclear explosion. It was actually a steam explosion that happened inside a nuclear reactor. There was no fire, but a huge steam-blast scattered all the nuclear fuel and nuclear waste into the Pripyat area. In other words, the Hiroshima bomb activated and used up its nuclear fuel in the blast, while the Chernobyl event covered the area in un-reacted nuclear fuel i.e. stuff which still contains its nuclear energy.
The specifics are quite complex because it relates to the different types of atom being turned into other types of atom but the way to think of it is that Hiroshima used up most of its "dangerousness" in the blast while Chernobyl just seeded the land with dangerous stuff, still ready to poison you!
Furthermore, the amount of nuclear fuel at Chernobyl was closer to 163,000 kilograms (rather than the meagre 0.9 of Hiroshima). Although Hiroshima might seem like a more terrifying event, Chernobyl involved a much larger amount of nuclear material. So it's like the difference between quickly blowing up one piece of coal (looks more spectacular but it's not a huge amount of fuel) as opposed to taking a mountain of coal and gradually burning it slowly for many years (looks less impressive but it's going to last longer).
The other main factor to consider is that both the Hiroshima and Nagasaki bombs were actually detonated mid-air, meaning that a lot of the nuclear material was blown and scattered around by the wind. Over time, it was carried away and diluted until both cities returned to normal background levels. By contrast, the Chernobyl event happened on the ground and a lot of the nuclear material was sprayed around the local area and went into the rivers, plants, soil etc. This means a lot of the nuclear material is still there, in the ground and in the water.
It's worth noting that a lot of animals are living in the abandoned Chernobyl site and honestly, nobody's quite sure why. It's possible that people have overestimated the effects of radiation exposure, perhaps the world's ecosystems have a way of taking care of themselves we don't know about or, maybe, a lot of these animals have somehow developed some advantageous mutation which makes them less susceptible to radiation poisoning (probably unlikely, but at the moment, we have to consider any plausible hypothesis).