The one thing you can rely on is that the Bitcoin API isn't easy to use for the non-specialist programmer. There are already libraries that make it easier, but Chain aims to create a Restful API that you can use from just about anywhere.
The new API is designed to make it easy to create applications that make use of the block chain. A Bitcoin, or any crytpo currency based on bitcoin technology, uses a distributed block chain to verify and record transactions.
The algorithm used is a solution to the Byzantine Generals' Problem, but essentially it uses a cryptographic proof of work to avoid simultaneous updates and to make central control difficult. In essence, the block chain is a ledger or transactions that have been validated without a central authority managing the system.
The block chain algorithm has been hailed as a huge breakthrough just waiting for people to wake up to its importance and start to innovate. The difficulty of the API is a barrier to innovation and this is where the Chain API comes in. It isn't designed to initiate a transaction or to create a Bitcoin wallet. What it does is give access to the Bitcoin block chain.
Chain does most of the work on its servers and then delivers the block chain to the programmer via a Restful API. So far it only supports Bitcoin, but there are plans to extend it to Litecoin, Dogecoin and Namecoin.
Currently there are only three API calls - Address, Transaction and Blocks. The Address call returns basic info given an address hash. Transaction does the same for transaction and Blocks for a block. For some applications this might seem limited, but Chain promiseS a dozen more functions as well as support for the other currencies in the near future.
Exactly how revolutionary the Bitcoin algorithm turns out to be is a matter for debate and some skepticism, but making it easy to use at least lowers the entry level.
At the moment access to the servers is free while the system is in beta. After that who knows?