the most important difference is that 'an accident' is something which happens purely by chance, there was no intention involved, and we can?t really use 'incident' like this.

If you do something by accident, you don't mean to do it, perhaps it's something you do or did without thinking.

Post-it notes, for example, are little sticky pieces of paper that we use to write notes on. And they were discovered by accident when a scientist, who was trying to make a very strong glue created a very weak one instead. He didn't mean to discover Post-it notes - he made them by accident.

We often use 'accident' to describe something unpleasant or unfortunate ?
"She had an accident while she was skiing and broke her leg."
It's especially common to use it when we are talking about traffic and vehicle collisions ...

"The car accident caused a big problem on the motorway."

'An incident' is much more general - we can use it to talk about almost anything that happens, any single event. If we were describing a particular time when something went badly wrong, we might talk about "the incident last summer" for example.
It might be something completely intentional - someone deliberately starting an argument ...

"We don't talk about politics at home since the incident last summer. Li was looking for an argument and brought up the subject of the recent elections."

We couldn't call the argument 'an accident' because Li started it deliberately.

We often say 'incident' when we don't want to mention what actually happened, or sometimes if we want to make an event sound less important. The police use 'incident' to talk about possible crimes, if they're not yet sure if a crime has been committed. It's quite common to hear:

"Police are looking into the incident."

It means that they are investigating to see if someone has committed a crime.

So the biggest difference is that accidents are never intentional, but incidents might be!