What is a second level domain?
A second level domain is a domain that sits under a top level domain like .com or .uk.
In the past a good second level domain was considered essential when registering a domain name, however with the proliferation of new gltds, and google's emphasis on good content and authoritative links, it is no longer the case that a second-level domain like insurance.com is incredibly valuable. Nobody types in insurance.com if they're looking for insurance, they type insurance into a search engine, which has radically different results and depends on your location and other interests. For example insurance.com is not even on the first page of google results for 'insurance'. So it's more important to consider what your domain name tells potential customers seeing a link than how it affects your search ranking or how prestigous it seems.
Country second-level domains
Many country codes don't allow registration of second level domains directly, and instead offer a selection of second-level domains which you can register a public domain under.
For example, the United Kingdom allows .ac.uk for academic domains and .co.uk for commercial domains, and many other second-level domains restricted to specific purposes, for example nhs.uk is restricted to the National Health Service. Brazil has over 60 second-level domains for many different uses which are more restrictive. France has avocat.fr for attorneys, veterinaire.fr for vets etc. If you want a geography-specific domain, you may well want to look at the second-level country domains in the country in question, and choose one appropriate for your project. IF you want a global domain, you should avoid these country-specific second level domains.
Although many of these second-level domains come with restrictions in practice many of these old restrictions are poorly or not at all enforced, so that you can register many domain names without formal proof of your identiy as the entity the domain was intended for. This varies by country and domain, so research what restrictions exactly your chosen domain imposes before trying to register.