How broad is the term statistical summary? I am wondering how broad is the term "statistical summary". For example, can a set of inferential statistics, descriptive statistics, along with both parametric and non-parametric density estimation, be considered a statistical summary? If a "statistical summary" doesn't encapsulate this whole set of abstractions, is there a better term?
 A: I do not think it is a term for which there is a widely accepted definition. So, unless your specific field has a commonly used meaning for the term, you can probably use it flexibly.
If a document had this heading, I would not find it particularly weird to see what you described in your example under this heading. I would probably normally prefer "Results" or "Summary of results", but if there are multiple types of results, some further distinction might be needed. E.g. if there are qualtitative results from interviews, as well as results from statistical analyses for some other research, then perhaps "Summary of quantitative results", "Results of quantitative analyses", "Results of statistical analyses", "Statistical summary" or any other similar term is a reasonable heading for a section describing solely the latter type of results.
A: Below is Minitab's 'Graphical Summary' of 100 observations chosen from the distribution $\mathsf{Norm}(\mu = 100,\, \sigma = 10.)$ It gives more extensive results than those from describe as mentioned in my Comment. 
[This summary seems to have been planned with the possibility of normal data in mind. It automatically includes a test of normality and confidence intervals for mean and standard deviation assume normal data--even if data fail the normality test.]
Several other software packages
give similar information, but not always labeled as a 'summary' and not always with the same list of information. In SAS, proc univariate gives several pages of output.
This gives you a general idea, but I am not aware of any standard definition
of the word 'summary'.

Note: The normal density curve superimposed on the histogram estimates the population mean $\mu$ by the sample mean $\bar X$ and the population standard deviation $\sigma$ by the sample standard deviation $S.$ If the data were from an exponential distribution the normal curve would tend to be a poor fit to the histogram, and the confidence intervals for mean and standard deviation would be inappropriate.
