This is the 6143rd most frequent Russian word.
судебный
"Judicial" or "pertaining to court."
Here, 'судебный' is used as an adjective to describe the process ('процесс') related to legal or judicial matters.
Судебный процесс начался вчера.
The court case began yesterday.
In this sentence, 'судебное' describes 'разбирательство', emphasizing its nature as being connected to judicial actions.
Судебное разбирательство затянулось на месяцы.
The legal proceedings dragged on for months.
'Судебные' in this context qualifies 'органы', referring to entities responsible for judicial functions.