Dispersion parameter in GLM output I have ran a glm in R, and near the bottom of the summary() output, it states
(Dispersion parameter for gaussian family taken to be 28.35031)

I've done some rummaging on Google and learnt that the dispersion parameter is used to fit the standard errors. I'm hoping somebody could provide more details on what the dispersion parameter is and how it should be interpreted?  
 A: Let us speculate the simple situation where there is no covariate information in your data. Say, you just have observations $Y_1, Y_2, \ldots, Y_n \in \mathbb{R}$.
If you are using normal distribution to model your data, you would probably write that 
$Y_i \sim \mathcal{N}(\mu, \sigma^2)$,
and then try to estimate $\mu$ and $\sigma$, maybe via maximum likelihood estimation.
But let's say your data is count data and thus not normally distributed. It is not even continuous this case, so you may use Poisson distribution instead:
$Y_i \sim Poisson(\lambda)$.
However, you have only one parameter here! The single parameter $\lambda$ determines both mean and variance by $\mathbb{E}[Y_i] = \lambda$ and $Var[Y_i] = \lambda$. This also happens when you use Bernoulli or binomial distribution. But you may have larger or smaller variance in your data, possibly because observations are not truly iid or the distribution you chose was not realistic enough.
So people add dispersion parameter to get additional degree of freedom in modeling mean and variance simultaneously. I guess any textbook on GLM will give you more detailed and mathematical explanation about what it is, but the motivation, I believe, is pretty simple like this.
