Hi Roxana,
These are the Settings Jonathan is using in the Course, as far as I can tell.

Left is in Edit Mode and right is the same in Object Mode.
To get rid of the straight lines, enable those 2, now grey, icons, like Omar mentioned above.
It doesn’t really get rid of them, but ‘bends’ them, using the Subdiv.
You can’t see the Subdivided Wireframe and the ‘bend’ lines at the same time.