Telephony is basically any method you can use to speak to someone else over a distance. Of course it means all types of phones but also includes Skype and similar programs. A fixed line or a landline means a phone that is connected to a cable in a wall. The number is also the place. A mobile is any phone which uses signals and not a cable.

A mobile is your cellphone and fixed telephony is the landline leading into your home for a telephone that is 'fixed' and cannot be taken with you.