It can depend on the context, but the term utenza fissa is often used to denote a landline telephone number, for example see here or here.
Utenza is a generic term that means an account with some utility provider. A priori it could refer to electricity, gas or many other things. What makes me think it is referring to the phone number is the term fissa. In Italian a telefono fisso (lit. fixed phone) is a landline phone as opposed to a mobile phone (which is after all the only kind of phone you can move around). While there are other kinds of unmovable utilities, the only one which has commonly both a fixed and a mobile version is the phone.
Note that the term utenza fissa in this sense is rather bureaucratic and would never be used in common conversation. Normally people would say numero fisso instead or even just un fisso (lit. a fixed one).