The beautiful and pure Mary Morstan is a single woman in her late 20s who comes to Sherlock Holmes for help in solving a mystery. She and Watson fall in love. Watson thinks Miss Morstan is quite lovely but fears money will make it impossible for him to marry her. He says of their prospects, "worse still, she was rich." He fears she will think he is pursuing her as a fortune-hunter—for her money, not herself.

As for Mary, she is impressed by Watson's stories of being sent to Afghanistan as an army doctor.

The two are middle-class English people, conventional, and not as intelligent as Holmes. They are well suited to each other. However, Watson does worry that marrying Mary will separate him from Holmes and his adventures. Watson says to Holmes,

Miss Morstan has done me the honour to accept me as a husband

This makes the decidely unromantic and analytic Holmes "groan."

Mary Morstan and Watson love each other, but Watson feels the tension between romantic love and male bonding.

Dr. Watson's close, loving relationship with Mary Morstan highlights Holmes's lack of an emotional connection with those around him. This serves to reinforce the impression of him as a coldly rational, logical man who uses his masterful powers of deduction to solve crime.

Watson is clearly much in love with Mary, and this gives us an insight into his personality. He isn't simply Holmes's admiring sidekick; he is a man in his own right, a man with a wide range of feeling and emotion. This makes him much more believable as a character and more likable as a person. Unfortunately, it doesn't make him much help when it comes to solving mysteries. That particular privilege is reserved for Holmes, who remains as devoid of any deep emotional life as ever.

Conan Doyle seems to have had little need for romance.  Mary Morstan is introduced in The Sign of Four as a romantic interest for John, and she is mentioned here and there after that until she seems to have died.  She does not seem to play an important role except in this first appearance.

It’s pretty clear that despite his desire to remain professional, John Watson is quite smitten with Mary Morstan.  Even before he admits he likes her, it is evident from his description. 

After the angelic fashion of women, she had borne trouble with a calm face as long as there was someone weaker than herself to support. (ch 7)

Watson is committed to helping Miss Morstan with her problem, even if it means he probably cannot get to know her better because she will be rich and above his station (very important in Victorian England). 

While there was a chance of recovering it I was ready to devote my life to the one object. True, if I found it, it would probably put her forever beyond my reach. (ch 8) 

John does propose, and Holmes’s reaction is to groan and say, “I feared as much.” (ch 12).  For Holmes, “love is an emotional thing” and he cannot let it interfere with his reasoning.  Watson seems to have no such problem, and when she dies later he is deeply affected by it.  Doyle makes little notice of it.  Perhaps he agrees with Holmes when it comes to women.