Offshore hosting simply refers to servers physically located outside your home country. The primary motivation is often legal or jurisdictional - avoiding domestic laws on content, data storage, or taxation. A US company might host in Iceland to avoid US data retention requirements. A UK company might host in Romania to avoid UK copyright enforcement. The server's location determines which laws apply to the data and content.
Offshore hosting does not necessarily mean permissive content policies. A server in Germany is offshore for a US client but will comply with US DMCA requests, EU copyright directives, and German domestic law. Being in a foreign country does not automatically make a host bulletproof.