There are plenty of answers on SO and good posts on the web about mocking. One place that you might want to start looking is the post by Martin Fowler Mocks Aren't Stubs where he discusses a lot of the ideas of mocking.
In one paragraph - Mocking is one particlar technique to allow testing of a unit of code with out being reliant upon dependencies. In general, what differentiates mocking from other methods is that mock objects used to replace code dependencies will allow expectations to be set - a mock object will know how it is meant to be called by your code and how to respond.
Your original question mentioned TypeMock, so I've left my answer to that below:
TypeMock is the name of a commercial mocking framework.
It offers all the features of the free mocking frameworks like RhinoMocks and Moq, plus some more powerful options.
Whether or not you need TypeMock is highly debatable - you can do most mocking you would ever want with free mocking libraries, and many argue that the abilities offered by TypeMock will often lead you away from well encapsulated design.
As another answer stated 'TypeMocking' is not actually a defined concept, but could be taken to mean the type of mocking that TypeMock offers, using the CLR profiler to intercept .Net calls at runtime, giving much greater ability to fake objects (not requirements such as needing interfaces or virtual methods).
Prologue: If you look up the noun mock in the dictionary you will find that one of the definitions of the word is something made as an imitation.
Mocking is primarily used in unit testing. An object under test may have dependencies on other (complex) objects. To isolate the behavior of the object you want to replace the other objects by mocks that simulate the behavior of the real objects. This is useful if the real objects are impractical to incorporate into the unit test.
In short, mocking is creating objects that simulate the behavior of real objects.
At times you may want to distinguish between mocking as opposed to stubbing. There may be some disagreement about this subject but my definition of a stub is a "minimal" simulated object. The stub implements just enough behavior to allow the object under test to execute the test.
A mock is like a stub but the test will also verify that the object under test calls the mock as expected. Part of the test is verifying that the mock was used correctly.
To give an example: You can stub a database by implementing a simple in-memory structure for storing records. The object under test can then read and write records to the database stub to allow it to execute the test. This could test some behavior of the object not related to the database and the database stub would be included just to let the test run.
If you instead want to verify that the object under test writes some specific data to the database you will have to mock the database. Your test would then incorporate assertions about what was written to the database mock.