Halliday & Hasan (1976: 22-3):
The more specifically we can characterise the context of situation, the more specifically we can predict the properties of a text in that situation. If we merely name the subject–matter, or the medium, it will tell us very little; we could talk of a 'register of marine biology' or a 'newspaper register', but this hardly enables us to say anything of interest about the types of texts in question. But if we give some information about all three categories of field, mode, and tenor, we begin to be able to make some useful observations. If we specify a field such as 'personal interaction, at the end of the day, with the aim of inducing contentment through recounting of familiar events', with mode 'spoken monologue, imaginative narrative, extempore' and tenor 'intimate, mother and three-year-old child', we can construct a great deal of the language of this kind of bedtime story…
The register is the set of meanings, the configuration of semantic patterns, that are typically drawn upon under the specified conditions, along with the words and structures that are used in the realisation of those meanings.
That is, registers can be identified by the contextual features that describe the type of situation that the register realises.
But, note, however, that registers are meaning (semantics) realised in wording (lexicogrammar) — not the features of field, mode and tenor that characterise the context in which the register functions.