The reason it is more than a database is because it provides more than the structured data storage that is provided by databases.
At the core of Tigris is a transactional document database built on FoundationDB. Then Tigris automatically indexes the data so you can run search queries (think Elasticsearch) without having to pipe the data to Elasticsearch. Tigris also provides an integrated event streaming system so that you can build event-driven applications (think Kafka, Google PubSub, etc). The beauty of the event streaming system is that you can then also run search and read queries on the events data automatically.
We have explained the high level architecture here: https://docs.tigrisdata.com/overview/architecture