Theory:

“Then you know practically nothing about my aunt?” pursued the self-possessed young lady.

“Only her name and address,” admitted the caller. He was wondering whether Mrs Sappleton was in the married or widowed state. An undefinable something about the room seemed to suggest masculine habitation.
Explanation:
 
After Mr Nuttel explained how the place was foreign to him, Vera wanted to know whether her aunt- Mrs Sappleton- was also a stranger to him. So she asked, "Then you know practically nothing about my aunt?"
 
Mr Nuttel admitted that he knows only her name and address. It explains how he came to know about her from the cover of ‘the letter of introduction’, where the receiver's name and address appear.
 
Meanwhile, Mr Nuttel was curious as to whether Mrs Sappleton was married or widowed. Unmistakably, the title "Mrs" explains that Mrs Sappleton is not unmarried. She had to be married but could also be a widow. The question here is not about Mrs Sappleton's marital status but rather about the presence of a man in the house.
 
There could be various reasons why Mr Nuttel had such a thought. Given that he is a shy and resistant person, he might have thought that he would be more comfortable around someone of his gender. On the other hand, as it was a young girl who had been keeping him company, he might have deduced that there was no man in the house at present. Had there been a Mr Sappleton, he would have played the host instead of Vera.
 
Nevertheless, Framton Nuttel sensed "masculine habitation" in the house. Though he couldn't place his finger on it, "an undefinable something about the room" indicated that a man resides there.
 
The phrase "undefinable something" is what one may call intuition. Intuition is 'the ability to understand something instinctively, without the need for conscious reasoning’. That is, it doesn't mean that intuition is baseless or irrational. Instead, our brain works on different levels: conscious and subconscious. While the data that the conscious mind collects can be easily reasoned out, the details collected by the subconscious mind cannot be. Such details picked by our subconscious brain is known as intuition.
 
Hence, one mustn’t dismiss one’s intuition and instinct.
 
Meanings of difficult words:
 
S.No
Words
Meanings
1
PursueFollow or chase someone or something
2
CallerA person who pays a brief visit
3
Masculine
Having qualities or appearance traditionally associated with men
4
HabitationThe act of living in a particular place
Reference:
National Council of Educational Research and Training (2008). The Open Window – Saki (pp. 55 - 61). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.