Level 2 Helpdesk Support primarily deals with issues which requires deeper level investigations and access to various configuration files. They also handle escalated issues from basic help desk support queue and escalate the necessary tickets to the advanced help desk support team.
For web hosting business, this level of support often demands root level shell access. Issues which can be resolved through the admin interface of any control panel too falls in this category. For eg: a primary domain change in a cPanel based server, would require WHM access to change the domain name and even though 90% of the time, it is an easy task, Level 2 helpdesk support helps in solving the issues raised for the 10% time as well.
For a product based support, Level 2 support techs will have more technical knowhow on the inside outs of your product. Training shall we given in such product based support for the techs to answer Level 2 issues.