At the time of writing, there's no clear statement on to what extent it will be open source. It will be built using and based on a lot of open source components, yes, e.g. OpenGL, Linux kernel, QML, etc.

It may consists of some closed source parts for various reasons: firmware for hardware support, a way to improve security (not discussing if that would be a good idea here), etc.

If [Ubuntu OS would be entirely open source], how could mobile carriers like AT&T lock the phone to work only with their SIM?

Open source software and a SIM-lock aren't really related here.

The radio part of a phone is a completely independent piece of hardware. The SIM-lock is usually in there, rather than a check in software. It can be controlled (locked/unlocked) however with hardware-specific calls to this. Android is no different in this, as the kernel-level here is also Linux (GPL).