Weebly is a site builder that allows you to create websites quickly and easily. You get to choose from a number of nice looking themes, and then you can create pages and drag-and-drop various elements (paragraphs, pictures, videos, forms...) to them. You can do this even if you have no knowledge of HTML or CSS.
For those who wish to delve deeper, Weebly does allow to edit the HTML of the theme to some extent, as well as gives you access to edit the CSS file. But keep in mind the things you can change are limited; for example, some webpage elements are described in a second CSS file that comes from Weebly that you can't change. If you want full control, it's always better to host a website on your own.
I was pretty impressed with Weebly, but also ran into some problems right away. Weebly allows you to add pages as well as blogs to your site - but it seems it's not quite ready to be used as a full-fledged blogging platform. The biggest problem I've encountered is the mess with meta descriptions and titles for blog posts.
You see, Weebly allows you to enter custom meta description and title for every page. However, it treats blogs as pages, too. What this means is that if you enter a title ("My Blog") and meta description ("I blog about stuff here, check it out") not only your blog's homepage will have it, but also every single post on your blog.
Duplicate meta descriptions and titles on every blog post is a pretty bad thing. If you use Google's Webmaster Tools, they will quickly point out this problem in Diagnostics > HTML suggestions as well. My conclusion is, if you want to make a simple webpage, or even an e-commerce website, Weebly might suit your needs just fine. But if you're looking for a blogging platform, it's not quite up to par yet.
Shameless ad: if you signup through my affiliate link, we'll both get 1 month Weebly Pro membership. Cheers.