Theory:

Macavity, Macavity, there’s no one like Macavity,
For he’s a fiend in feline shape, a monster of depravity.
You may meet him in a by-street, you may see him in the square —
But when a crime’s discovered, then Macavity’s not there!
Explanation:

The fourth stanza begins with the refrain, "Macavity, Macavity, there’s no one like Macavity". The speaker explains why there is no one like Macavity. According to the speaker, Macavity is a terrible criminal and is a devil in the shape of a cat. Furthermore, the speaker calls him a 'depraved monster', meaning he is an animal with no moral values.
 
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Macavity is a devil in the shape of a cat

Though Macavity is known for his ability to remain hidden, it doesn't mean that he is always in his hideout. One is likely to see him in private streets or crowded places, but once his crime is detected, he escapes and becomes the mystery cat, and he is impossible to locate. Thus, again, the stanza ends with the refrain: "Macavity’s not there!".
 
Meanings of difficult words:
 
S.No
Words
Meanings
1
Fiend A person (or animal) of great wickedness or maliciousness; a terrible person who can be likened to a demon; criminal
2
Feline Of relating to cats or the cat family
3
DepravityThe state of being morally bad, or an action that is morally bad
4
Square An open, typically four-sided, area surrounded by buildings in a village, town, or city
5
Monster Someone who is very cruel and evil;  (in stories) an imaginary creature that is very large, ugly and frightening
6
By-streetA street that is lead away from the main street; a private street or road
7
HideoutA safe place for hiding, especially from the law
Reference:
National Council of Educational Research and Training (2008). Honeydew. Macavity: The Mystery Cat - T. S. Eliot (pp. 50-51). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.