When discussing ISPs or Service Providers (SPs)
Tier 1 = webserver level(Client)
Tier 2 = application level(Host)
Tier 3 = database(Host)
Usually T1 faces the Internet, and forwards requests to the application servers. Application servers use the database. Typically you have a firewall between all 3 levels.
In the IT Business or Helpdesk service
Tier 1 refers to all technicians regardless of term of employment. There are no manuals. This is the basic troubleshooting level. (ie. check settings, account status, run diagnostics).
Tier 2 is the level that a problem is escalated to when it is determined not to be a problem on the users end or beyond the power of a Tier 1 tech. Usually these are the people that are in direct contact with the administrators.
Tier 3 are the administrators themselves who are contacted when it is determined to be a server/DNS/authentication problem.