Theory:

Thus ending, he hastily lifted the wicket,
And out of the door turned the poor little cricket.
Folks call this a fable. I’ll warrant it true:
Some crickets have four legs, and some have two.
Explanation:
 
The ant refused to help the cricket. He quickly closed the small opening in the door and shut the cricket out of his house. The poor cricket had no other choice, but to leave the place.
 
The poet says people think of this story as a fable (an imaginary story), but he feels it could have even really happened. The moral of the story is very true that it can happen actually in real life too. He refers to the cricket in the poem as a four-legged cricket, and humans as two-legged crickets. If we are silly enough like the cricket, we will also end up starved and disappointed. We should always think ahead and save for the future.
 
Meanings of difficult words:
  
Words
Meanings
wicketan opening in a door, gate or wall
hastilyurgently, quickly
folks
people in general
 
Rhyming words:
 
  1. wicket - cricket
  2. true - two
Reference:
National Council of Educational Research and Training (2008). Honeydew. The Ant and the Cricket - adapted from Aesop's Fables (pp. 21-23). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.