State-sponsored attacks are hacking incidents that are backed up or supported by government organisations/agencies. Often they support these attacks to gather information on the general public.
These state-sponsored actors may target activists, anonymous members of the public and random members of the public. The actual information these state-sponspored actors will try to obtain are names, email addresses, phone numbers, birthdays and other personal information used to identify you.
Government organisations can use this information to track and locate certain activists wanted by security agencies such as MI5, G4S or the police.
If your website/service comes under attack from a state-sponsored actor, it is almost impossible identify what government supported the attack. Some notorious governments known for these attacks are Russia, China, Great Britain and The United States.
If you do come under attack from a state-sponsored actor, it is recommended that you fix any vulnerabilities/security risks in your service as soon as possible to protect you and your users from government spying/hacking programs aiming to gain your personal information for illegal uses.
Hacking is still illegal, even if they are in a position of authority / government power.