This is the 7414th most frequent Russian word.
гражданский
"Civil" or "civilian."
Here, 'гражданский' is used as an adjective to describe a conflict involving citizens or pertaining to civil affairs, distinguishing it from military or international issues.
В стране произошёл гражданский конфликт.
A civil conflict occurred in the country.
In this context, 'гражданский' modifies 'law' to convey the domain of law dealing with private rights and matters, as opposed to criminal or administrative law.
Она изучает гражданское право.
She studies civil law.
'Гражданский' here is applied to protests to indicate that they are initiated by citizens advocating societal or political demands, maintaining the focus on the civilian aspect.