Level 2/3 - Software Engineer: Entry level engineers. Need to be individual contributors. Typically involves, gaining command of all core Google technologies. Need to be able to start developing and production-izing low to moderate complexity modules by working as part of a team.
Level 4 - Senior Software Engineer: Reasonable command of Google technologies. Shows comfort with owning reasonably high complexity modules. May be a tech lead of a small team/project. Be able to mentor engineers in the team, giving technical guidance, code reviews, and ultimately be able to take responsibility of delivering small projects end-to-end on production.
Level 5 - Staff Engineer / Level 6 - Senior Staff Engineer: From these levels, Google's coveted levels start. Staff engineers and above comprise, say just about 10% of all of Google engineering. A Staff/Senior Staff Engineer is one with a reputation of being able to work on complex Google software. They may lead complex initiatives and technically lead teams towards implementing and productionizing them. Typically staff engineers are seen to be very strong individual contributors who also set the bar for a team for technical excellence and delivery. Starting now, roles also become fairly visionary in that, engineers may come up with ideas to expand their projects and may also have a reasonable free-hand in developing and executing on them (or in rarer cases, even brand new ideas for Google products). The difference between 'staff' and 'senior staff' may be just about the impact/complexity scale of the project.
Level 7- Principal Engineer / Level 8 - Distinguished Engineer: These are much higher impact roles. Such engineers have owned and delivered on very large mission-critical projects for Google (Think significant search engine/ads optimizations that have in a verifiable way, impacted Google positively). They are responsible for initiating, driving, technically designing, implementing and productionizing high impact ideas at Google with the help of teams if needed.
Level 9 - Google Fellow / Level 10 - Senior Google Fellow (added in '13): The most coveted engineering role at Google. These are publicly known names of a handful of people who have built an excellent reputation for being the top technology visionaries at Google, having built very renowned products/ideas at Google and have in tremendous ways influenced the success of Google. Think Jeff Dean.