Many proofs in cryptography start with the following assumption: assume x is a bitstring of length N drawn from a uniformly random distribution of bit strings. This assumption is then used as the basis of the proof of the cryptographic construct.
For instance in a provably secure stream cipher you start with that assumption then proceed to show that if weak one-way-functions exist then you can construct a secure pseudo random number generator that is polynomially indistinguishable from a true random source. You then use your assumed random bit string, x, as the key to the psuedo random number generator to generate a one time pad to XOR with your message.
Since the secure psuedo random number generator is indistinguishable from a true random number generator (by a polynomial attacker) the message is secure (from a polynomial attacker). However, this is all predicated on the key being drawn from a uniform distribution. If the key is NOT drawn from a uniform distribution than there may be a potential speed-up available to the attacker.
What the paper shows is that often it is assumed that words drawn from an IID distribution of letters can be treated as if the distribution of words is uniform (given a sufficiently large word size). However, this distribution while very flat is not quite uniform. They show how this can be exploited using the "Guesswork" framework to come up with a tighter bound on the time it would take to guess a chosen word. This bound is much better than the traditional bound used.
What this means is that there needs to be more margin given than previously thought when dealing with keys derived from non-uniform distributions. Such keys include passwords.