Enfield and Utterson are distant relations who share a similarity of temperament, suggesting that their temperament are a long established family trait owned by many predecessors. This is important to the story since Utterson is set up as the counterpoint to Hyde: They have similar traits of coldness, but Utterson's eyes are sparked by "something eminently human" that may not show itself in his conversation but does however show itself in his actions; quite the contrast to Hyde.
Enfield and Utterson, two dark brooding men, the former (Enfield) endowed with a social inclination and a Hyde-like love of adventure that the latter (Utterson) lacks, are inseparable and utterly devoted to each other, proving in double exposure that dark brooding natures do not exclude the human qualities of love, compassion, loyalty, mercy and unity of soul just by virtue of their character traits and natures. This relationship of loyalty and deep human virtues dramatizes the inhumanity of Mr. Hyde and underscores the falsity of Dr. Jekyll's experiments.
Enfield and Utterson are companions and confidants who dearly enjoy each other's company, and cling tenaciously to their Sunday walks. Stevenson uses Enfield's social nature to acquaint Utterson with the existence and nature of Hyde and the reader with a outsider's perception of Mr. Hyde.