First, I believe "cloud" in the context of the blog article you read should really be more granularly defined as Azure. There are several cloud solution offerings and Azure is only one although it is gaining immense popularity in the MS community space. The Azure cloud is fairly unique compared to products like Amazon's cloud in that it requires applications that use it to comply to a specific set of APIs. To build an application for azure requires you to embrace certain architectural principles from the beginning and to build your app using its web and worker roles. To "fit in" to these roles, your app must be built within a special VS project that references the Azure SDK.
If you were to use another cloud solution like Amazon, it is more similar to firing up a VM or group of VMs that can host your app as is without the constraints of specific APIs. You simplu would fire up a windows server instance, install what you need on it like any other server you would use in a hosted or or leased data center environment.
I am not implying that the azure solution is flawed or overly restrictive. Rather, I think it supports some architectural constraints that will allow you to "fall into the pit of success." However, it may be difficult to effortlessly migrate many brown field apps to azure without making significant changes.
As far as why host a application in the cloud as opposed to a normal hosted environment. It really depends on your app, your business/budget constraints and your traffic level. For many small, hobby sites, you may be better off keeping your app on a traditional hosted environment. For larger scale apps, the cloud begins to make more sense. The cloud is really supporting a "pay per use" model. If you need to have the ability to scale out quickly without the funds or the ability to wait on a purchase of lots of additional hardware, the cloud is a good option. Cloud providers have deep pockets and plenty of server resources and bandwidth to send your way at a moments notice that you can rent instead of buy.
Also, because cloud providers are large and typically highly reputable, they can afford to hire expert staff and follow best practices that you may not be able to afford on your own. They can and will handle a lot of the day to day ops administration enabling you as a developer to not have to think of things like security and redundancy.
So as I see it, cloud solutions are ideal for apps that are beginning to see a fair amount of traffic, need guaranteed up time, and do not want to pay or bother themselves with their own admin staff, server purchasing and data center management. I think they are not practical for many small hobby sites and once you become really big, bringing your app on site with your own staff may become more economical.
That all said. it has become "cool" in the .net space for any site to run on azure. I'll admit that some of the architectural models are interesting and seem fun to work with. However, if you take a close look at the pricing model, you may find you are better off with your hosted plan.
