Something inevitably happens because it's going to happen eventually, and there's no way to stop it.
So when people say "inevitably" they usually mean that an event or situation is unavoidable. You might hear someone talk about a project that will inevitably be delayed because of a shortage of resources. Or maybe you'll see a news headline saying that climate change will inevitably lead to more extreme weather events. In both cases, the speaker is just stating what's going to happen based on the facts and circumstances.
In some cases, "inevitably" can also mean "as a natural consequence". For example: "She gained weight inevitably because she didn't have time for exercise." Here it means that gaining weight was the direct result of her busy schedule.
In a manner that is impossible to avoid or prevent.
Example: Despite the town's best efforts, the dam inevitably gave way.
