You have your own site, maybe even host it internally. You need to implement a blog/calendar/etc, and you need to do it on the cheap. Doing this cheaply means that you want to be able to budget a given amount for the feature, and know that it won't change. In other words, you want to spec $x, and you want to avoid risk. The risk in this case are the development/implementation costs, and more importantly the maintenance costs. Maintenance costs have been noted for being considerably higher than the cost to build and implement a system.
Use Case #1
You have a need to add an events calendar to your site. You have someone that manually updates the site every day or two, and manually adds and removed calendar entries to your home page. They then create a new page for each event, and delete pages for old events. This is a little tedious, especially since you know what all the events are 6 months ahead of time, but only want them visible on your site 2 weeks in advance.
Problem solved. The cost is a small monthly maintaince fee.
Use Case #2
This case extends case #1 above. The additional requirment/problem is that this calendar will not only appear on your site, but also on 3 other affiliate sites as well as some internal pages on your site.
The solution of course is the same as the first.
Use Case #3
Same problem as case #1, but you already have an admin tool that must be used to administer your calendar. You have developers that could provide this functionality, but you want to save some costs, and prefer to have a hosted provider worry about monitoring and maintenance of the system.
Solutions like these are popping up all over the place as free tools. The problem is that "free" usually means advertisements or branding is added to the calendar on your site. You are also given limited presentation controls in most cases. Free also means that it will go down sometimes, and that there is no expectation of longevity. These services are often marked with the Web 2.0 moniker "beta", and in this case "beta" is a bad thing.