The name Markdown is of course a play on markup, with the implication that it’s somehow less: less work, not to hard to understand. For very simple documents Markdown can indeed be easy. In the manner of DEC NotesFiles from the 1970s and 1980s, one uses ASCII symbols for *bold* and _italic_. Hypertext links are more complex, and tables are supported only in some of the Markdown variants and can be a nightmare to use in a text editor. The primary context for using markup is where people edit the text directly in a plain text editor and this means that it is really only intended, and only suitable for, simple documents. If you are using a tool that edits Markdown and hides the syntax then you might as well be editing HTML or XML: the primary reason to use Markdown files is that you have tools, such as github or a wiki of some sort, that consume it.
Since there are no special tools needed, and since Markdown can really only cope with simple documents, the syntax can be easy to learn and training costs can be low. Markdown is generally close to a subset of the format used by Wikipedia, so, with extensions as needed, it can clearly scale.
The semantics recorded in Markdown is purely operational: go bold, go italic; whilst some variants have additional tagging support, the primary assumption is that the appearance of the document (or the sound, when read out loud by text to speech) is primary.
Markup is fabulous, though, for very simple README documents for projects such as computer source code, where the file can be read easily in a plain text viewer or editor without any special tools.
If you choose to use Markdown for a project, be aware there are competing versions and make sure you have a fully compatible tool-set if you need one. If, however, you have figures, tables, footnotes, cross-references, running page headers (or even page numbers), or other features that go outside the normal remit of Markdown, or if you foresee a need to reuse the information and extract information from the text, you will almost certainly be better off with a richer format.
If necessary, you can provide a tool to read a specific version of Markdown and convert it to (say) XML-encoded TEI documents for users in a text-based environment.