Jekyll is well suited for users who would like to have all content within source control (Git) along with the code used to produce the website. Because everything it produces is static assets (HTML, CSS, etc.), sites created with Jekyll are super fast, with very little needed on the server side of things. There are also a few really great free solutions for deploying and serving Jekyll websites. Jekyll will be tough to maintain for users who are not web developers, comfortable using Git to update content. There are 3rd party solutions for maintaining Jekyll-based sites without having to touch the code, but this will cost extra money. Also, because there is no server-side language, you will need to look elsewhere to handle things like contact forms.
Straight out of the box, Jekyll lacks a friendly WordPress-style back-end. You'll be working in Liquid (HTML), Sass (CSS), and Markdown (content) files. If you're already comfortable with these languages, you'll feel at home in no time. If not, you may need to consider getting someone else's expertise to set up the site, and then use another back-end (probably paid) to make editing your site's files less intimidating.
If you use GitHub Pages for the free hosting, be forewarned that GitHub only white lists a few plugins for their own compilation. This usually isn't a problem (you can compile on your own computer if need be), but can be annoying at times.
All the other CMS's I've used try to make it easy for the nontechnical user to manage a website, at the expense of adding complexity and weight to the system. Jekyll takes the exact opposite approach, eschewing all unnecessary complexity. If you know what you're doing in a code editor, Jekyll will probably feel like a breath of fresh air to you.
