I think this has a lot to do with it. After an hour of reading, watching and thinking, I can't come up with any way to put it into one paragraph.

Here's the shortest what and why I could come up with:

Questioning Assumptions

Many relational databases today operate based on assumptions that were true in the 1970s but are no longer true. Newer solutions such as key-value stores ("NoSQL") make unnecessary compromises in the ability to perform queries or make consistency guarantees. Datomic reconsiders the database in light of current computer set-ups: millions of times larger and faster disks and RAM, and distributed architectures connected over the internet.

Data Model

Instead of using table-based storage with explicit schemas, Datomic uses a simpler model wherein the database is made up of a large collection of "datoms" or facts. Each datom has 4 parts: an entity, an attribute, a value, and a time (denoted by the transaction number that added it the database). Example:

John, :street, "23 Swift St.", T27

This simple data model has two main benefits. It makes your data less rigid and hence more agile and easier to change. Additionally, it makes it easy to handle data in non-traditional structures, such as hierarchies, sets or sparse tables. It also enables Datomic's time model...

Time

Like Clojure, Datomic incorporates an explicit model of time. All data is associated with a time and new data does not replace old data, but is added to it. Returning to our previous example, if John later changes his address, a new datom would be added to the database, e.g.

John, :street, "17 Maple St.", T43

This mirrors the real world where the fact that John has moved does not erase the fact that John once lived on Swift St. This has multiple benefits: the ability to view the database at a point in time other than the present; no data is lost; the immutability of each datom allows for easy and pervasive caching.

Move Data and Data Processing to Peers

Traditionally databases use a client-server model where clients send queries and commands to a central database. This database holds all the data, performs all data processing, and manages the data storage and synchronization. Clients may only to access the data through the interface the server provides - typically SQL strings which may include a (relatively small) set of functions provided by the database.

Datomic breaks this system apart. The only centralized component is data storage. Peers access the data storage through a new distributed component called a transactor. Finally, the most important part, data processing, now happens in the clients, which, considering their importance, have been renamed "peers".

Queries are made in a declarative language called Datalog which is similar to but better than SQL. It's better because it more closely matches the model of the data itself (rather than thinking in terms of the implementation of tables in a database). Additionally, it's not restricted like SQL. It allows you to use your full programming language. You can write reusable rules that can then be composed in queries. Additionally, you can call any of your own functions. This is a big step up in power and it's made practical because of the distribution. If ran your query on central server, you'd have to be concerned about tying up a scare resource with a long-running query. When processing locally, that's not a concern.

When a query is performed that data is loaded from central storage and placed into RAM (if it will fit). Later queries can use this locally cached data for fast queries.

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That's definitely not all it does or all the benefits, but hopefully that's a good start.