To sue means to start a legal case against someone in a court of law, usually to get money or to make someone stop doing something.
Suing someone is serious and can be stressful. It usually means there is a big problem between people or companies.
Examples:
She will sue the company for not paying her.
He sued his neighbor for being too noisy.
The man sued the store for selling him bad food.
The cat sued the dog for taking its bed!
I will sue the sun for being too hot!
The superhero sued the villain for making a mess in the city.