For the computer scientists, mxTextTools looks an awful lot like a Turing Machine. On failure, the read head is restored to the same position it was at before the state evaluation. However, unlike a standard definition of a Turing Machine, one state can evaluate multiple tape symbols to decide on success or failure. And also unlike a standard Turing Machine, little state machines are typically nested inside one another, with success or failure propogating upward. The short characterization is that mxTextTools can do everything regular expressions can, plus some things regular expressions cannot.
Readers can get a better idea by diving into some code.
Or rather, it better match some pattern or it just will not know what action to take for the next bit of text. Let's walk through the lines above, this example is a good illustration of what mxTextTools does generally. The function gets passed arguments that tell it about the details of the match, if found. The second tuple element expresses two things in the example. The read head is advanced with each matching character encountered.