Sia is fundamentally a cloud storage platform. And, when compared to other types of cloud storage, it has the following advantages:
Decentralization. Only the uploader controls the files. Nobody can spy on the data, nobody can prevent you from downloading the data, and the data cannot be forcibly deleted from the network.
Price advantage. Uploading to Sia is extremely cheap. As of posting, storage was approximately $2.00 / TB / Month, which can be compared to Amazon's $21 / TB / Mo. Unlike Dropbox, Sia is metered, which means you only pay for what you use. 100 GB costs $0.20 per month, and 1100 GB costs $2.20 per month, etc.
Geographic diversity. When data is uploaded to Sia, it is uploaded all around the world. Outages due to DDoS attacks in North America don't affect the data, because it's also replicated in four other continents across a large number of nodes.
Sia makes the most sense for write-seldom, read-often data, however it is also a good substitute for most things that you would put on Amazon Glacier or Amazon S3. Here are some examples of things that work very well for Sia:
Computer snapshots. A computer snapshot often contains an enormous amount of personal information. Whether it's information about your friends, your health, your finances, or your passwords, you usually don't want corporations to have full access to your data, especially in a time when the new hot thing is to do as much data mining as possible. Sia's security can provide great peace-of-mind when backing up your computer to the cloud.
A media center. While security is not as much of a concern with media, media often takes up a large amount of storage, and Sia is one of the cheapest ways to store and retrieve data online. $2 per month gets you enough to store 1000 GB of media.
Research Data Warehouse. A lot of scientific research produces massive amounts of data. Whether it's genome sequencing, particle colliding, or something else, scientists are often forced to filter and discard valuable data for financial reasons. Cheaper solutions such as tape or Amazon Glacier often result in headaches and slowdowns when it's time for the data to be used. Sia as a platform is cheaper than both tape and Glacier, without needing to wait a long time to fetch the data.
More creative ideas:
Life recorder. A fun idea is to record your entire life through either a camera in your glasses or pocket or somewhere similar - such that your camera can see and record everything you do. This can create a mountain of data, and until the introduction of Sia this may have been intractable to store. However, storing an entire year's worth of SD video (480p, 8 hours per day) on Sia would only cost around $5 per month.
Web archive. Websites disappear, comments get deleted, data gets lost. Centralized archives preserve some of this, but often take snapshots infrequently and the data is stored in centralized places. Sia could potentially be used to save frequent snapshots of your favorite websites automatically, primarily being leveraged as a cheap backup source.
FUSE. FUSE would allow all data added to, removed from, or altered within a directory to be added to Sia with no further interaction from the user. Sia does not handle tiny files very well yet, so you would not want to run your entire computer out of Sia, however a FUSE implementation would be a great catch-all for all sorts of data, including programs, games, and web-downloads.
Blockchain database. It is possible to use Sia as storage for a blockchain. The Bitcoin blockchain currently stands at close to 100 GB, which can be a burden on your local machine but is very small compared to the scales of typical cloud storage. The raw blockchain data doesn't change, which makes it a great candidate for storage on Sia, and would be an excellent way to reduce the burden of running a full node without reducing the amount of security.