What does historical average mean as a general statistics concept related to history?

In this context, the historical average is unstated and could have been arbitrarily chosen by the author or inadvertently omitted. In stocks, for example, it's common to report average returns for periods like a month, 3 months, 6 months, one year, five years, ten years, year-to-date, since inception, etc., but if I just pick one without context, then I can easily choose the "historical average" that best supports my thesis. In the stated context, I suspect that the city's medical examiner has monthly averages going back many years and that year-over-year you would only suspect a small change (or a consistent "average"). This must have been considered a large change according to the author or his source.

Generally, "historical average", in a context such as "historical average death count in April", means that the counts for each month were separately averaged. Ie, all counts for January were averaged between, say, 1950 and 2018, all counts for February were similarly averaged, as were March, April, etc.

This approach is useful when the statistic being counted tends to have a regular yearly "pattern", say, rising in the winter and falling in the summer. Then the numbers from this year can be compared to see if there is a notable difference.

TLDR: It doesn't mean anything unless you tell us what it means.

Historical average is used to compare a recent statistic to an identical one from earlier data. For instance, if the average global temperature over the past decade was X, You can compare that to the historical average, which would typically not include data from the most recent decade (but this can be overridden by explicitly stating the date ranges of both). The dividing line between recent average and historical average should either be an explicit time, or an event that can be used to easily pigeon-hole the data as historic or recent.

Here's an example from The Average Annual Return in the Stock Market By: Carol Deeb, Updated April 19, 2017

Historical
Reviewing historical average annual returns gives you a big picture of the stock market over an 83-year period, as of the date of publication. In some 12-month cycles, the stock market, as a whole, earned increases of over 40 percent. However, in other years, investors experienced an average loss of about 4 percent to over 50 percent, depending on the year and the health of the economy. According to a report by New York University Leonard N. Stern School of Business, the historical average annual return for stocks from 1929 to 2010 is about 9 percent. When factoring in the return on Treasury bills, the average is 5.67 percent.

Recent
Recent average annual returns tell a different story than the historical percentage rates. In 2010, the NYU report shows that the average return on stocks alone was almost 15 percent, while Treasury bills were under one-fifth of 1 percent and bonds almost 8.5 percent. However, in the decade from 2001 to 2010, the average return on stocks and Treasury bonds together was a loss of almost 1 percent. Your return depends on the type of security that you are holding and the 12-month period in which you invest.