Theory:

Macavity’s a Mystery Cat: he’s called the Hidden Paw —
For he’s the master criminal who can defy the Law.
He’s the bafflement of Scotland Yard, the Flying Squad’s despair:
For when they reach the scene of crime — Macavity’s not there!
Explanation:
 
The speaker introduces Macavity to the readers. Macavity, as the speaker states, is a mysterious cat. He is also a master criminal. Moreover, like any notorious criminal, he has a nickname: Hidden Paw. The poem continues to explore and explain why Macavity is called a mystery cat.

Macavity, as stated before, is a master criminal who disobeys the laws enforced in the country. He commits crimes, breaks the rules, and indulges in mischievous activities, but he is so clever that he is never caught.

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Macavity defies the laws

The police force, referred to as Scotland yard, is constantly confused by his ability to disappear without a trace.
 
The phrase "Scotland Yard" refers to the police department of London. Hence, it is easy to assume that poem takes place in England.
Also, the speaker describes how the Flying Squad, known for its capability to reach a crime scene quickly, is sad and feels hopeless because Macavity is always faster than the squad. The police and the squad may get to the scene of a crime as quickly as possible, but, to their dismay, Macavity wouldn't be there.
 
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The police have a difficult time catching Macavity
 
The line "Macavity’s not there" is a refrain and is repeated throughout the poem.

The name Hidden Paw is important as it describes the nature of Macavity. The word "hidden" explains the cat's ability to remain hidden from the sight of the police. The word "paw", on the other hand, reminds us that Macavity is an animal, despite him being personified in the poem. Also, the phrase 'hidden paw' may suggest Macavity's ability to move around (using is 'paws') without being seen or heard ('hidden'). Hence, the name ‘Hidden Paw’.
 
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Paw prints
  
Meanings of difficult words:
 
S.No
Words
Meanings
1
Paw An animal's foot having claws and pads
2
Criminal A person who has committed a crime
3
Master criminal A clever criminal who is hard to be caught
4
DefyOpenly resist or refuse to obey
5
Bafflement The condition of being completely unable to understand or explain something
6
Scotland YardThe detective department of the London metropolitan police
7
Flying SquadA division of a police force or other organization which is capable of reaching a scene of crime or incident quickly
8
DespairThe complete loss or absence of hope
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.