Hi Sue, This is more linked to culture - as in many cultures calling someone by their first name (for example Tom, Sarah,..) as opposed to surnames or titles (for example Mr./Dr./Prof. Smith) is not something common, and is only acceptable if you are close to that person. In your example, being on 'first-name terms/basis' with someone means that they allow you to call them by their first name, which indicates you might be close to that person, or they may be very open; so if someone's distant, this may be hard to do! Hope this helps, Alex

She's very formal and he has to address her as Miss Lastname instead of using her first name.

Just to add some info: the term we use in the US is to "get on a first-name basis" rather than "get on first name terms."