EPUB is a versatile and open standard. For the casual user this means it can be used for free and there is good tool support for doing so fairly easily.
On a more technical level, EPUB is really just a zipped collection of files. If you change the .epub extension to .zip, you can open the file in many different zip compatible tools and see the individual files. Assuming, of course, that you're using an unlocked epub, one with no Digital Rights Management locking it down. So EPUB also supports protecting your work as well if you want to take that path.
The individual file contents of an epub will generally be many XHTML files, perhaps some image files, a style sheet that contains page layout instructions and a few other types are possible too.
Right now, you're reading this sentence in a web browser displaying HTML content. XHTML is pretty much the same but enforces a more rigorous tagging standard. Primarily, XHTML requires all tags to be closed where HTML does not. In many ways, an epub reader is like your web browser that converts the layout instructions of the web page into what you see on screen.
Most word processors will output your file in an HTML format. These HTML files can be converted into XHTML with some batch scripts and such to clean up the tagging. These converted HTML files are workable but not the best. We can work on those issues later as needed.
Because EPUB is widely supported, you can use your book on many devices however it's convenient for you. Epub readers include tools for searching the text, hyperlinking and adding your own notes. This gives you easy searchability for free without any complex indexing or related markup.
EPUB is a compact format. When I said that it's a zipped collection of files, I mean that the files are compressed through a ZIP algorithm. This saves space on your devices but on the small scale of an EPUB, does not incur a performance penalty.
EPUB content is reusable and flexible. People often worry about a file format becoming unsupported in the future. If you're using a particular recipe software tool, getting your content back out if that software stops production can be difficult. With an epub, XTHML files are just tagged text files. Your content remains readable and usable even if epub becomes obsolete. Nor are you locked into one vendor for reading or editing your content.
You can reuse individual files in your epub in yet another epub. So if you want to create a master cookbook that includes all your chicken recipes, you can do that. You might have individual files for different cuisines. Within the master cookbook, those file breaks can be invisible. You just see a Chicken dish after chicken dish, though the cuisine change will be clear. And you could reuse the Italian Chicken file in another EPUB that just covers Italian cooking for example.
You can have different layout, numbering, fonts and so on in these different EPUB. Because the numbering and such is controlled in a separate file from the XHTML in a well structured EPUB, your content is easily restructured to fit your uses.