The GraphHopper Directions API uses OpenStreetMap data, see the copyright with more details or TomTom data.
When using the OpenStreetMap road network we use Hole-filled elevation data from the SRTM project and elevation data from the U.S. Geological Survey.
The GraphHopper Directions API uses open source projects under the hood from GraphHopper GmbH, komoot GmbH, OpenStreetMap and many more, often under the Apache License 2.0. For example, jsprit or the routing engine, that themselves uses other open source components.
Our entire infrastructure is built on top of open source using Debian linux, Ansible, nginx, bash, python, git, Java and many more open source projects. Without them our services would not be possible. Thanks a lot!