>My understanding of monads, based on the examples in this paper, is that a monad essentially takes a series of computational steps and augments then with a secondary piece of data (a value to be printed, an error, etc).

Not really.

A monad:

1) helps translate values from one domain to another.

2) helps handle the logic in a series of operations.

One use of that is to enrich data with the possibility of carrying some other information (e.g. the Optional/Maybe that can carry an error). But that's not essential to what a monad does, and monads can be used for all kinds of things.

The description of a monad as a "programmable semicolon" captures that a little better. Semicolons in that phrase are meant to refer to the semicolons in C or Java, that separate different expressions.

So, in a program like:

  do this; do that; do another thing; ...

Monads helps pass values between the various steps, and help determine what happens with the sequence of operations (the program wont have actual semicolons between steps in Haskell e.g. -- it's just how we notate a number of expression in C-like style for example's sake).