What is the meaning of Mutual Information beyond the numerical calculation?
Two additional intuitive takes on mutual information:


When two random variables are independent the joint distribution $p(x, y)$ and the product of the marginal distributions $p(x)$ and $p(y)$ are identical. One could thus assess the degree of independent between two random variables by computing a probabilistic distance between $p(x) \times p(y)$ and $p(x, y)$ - this distance being 0 when the two variables are independent. A common probabilistic distance between variable is the Kullback-Leibler divergence. If you take the Kullback-Leibler divergence between the joint distribution and the product of the marginals of two random variables, you end up with... mutual information.
From a compression / coding perspective, imagine you are given a sequence of $N$ pairs of observations $(x, y)$. You want to compress them into a file. Two strategies: storing all the (x) in one compressed file then independently all the (y) in another compressed file ; vs compressing the pairs. Using an optimal coder, the file size in the first case is $N \times H(X) + N \times H(Y)$, while in the second case the file size is $N \times H(X, Y)$. The second approach is more efficient if there's a relationship between the two observed variables! How many bits have we saved per observation? $\frac{N \times H(X) + N \times H(Y) - N \times H(X, Y)}{N} = I(X,Y)$! So mutual information tells us how many bit per observation do we save by coding two data streams jointly rather than independently.


I am not sure about your example, though... Mutual information is computed between two random variables (distributions). I can see how "book" can represent the distribution of words in a book ; but I am not sure what "word" means here. Mutual information also requires "paired" observations to be computed.