You can either use a displacement modifier with an image as the texture
or use the texture as a “brush” texture in sculpt mode.
Both methods require that the base object has loads of geometry.
Your video is Zbrush so it uses a texture for sculpting.
Edit
After watching the video it is a bit different that displacement with a texture, they are using a 3d model to make the relief.
You could try this it is the most similar to the video:
