Can also be described as "interactive testing" - manual testing essentially means tests of any kind where a human is involved in the execution of the test.
Sometimes incorrectly confused with "user testing", possibly because some companies use "manual testers" to perform this kind of testing instead of real users.
Manual tests are required when assessing usability and are often applied for hard-to-automate features or when time constrains are becoming critical.
Related tags: exploratory
Read the following for an interesting critique of the term: http://www.developsense.com/blog/2013/02/manual-and-automated-testing/