"Leaf by Niggle" is very much an allegory of Tolkien's own creative process, and, to an extent, of his own life.
However, there are many mundane chores and duties that prevent Niggle from giving his work the attention it deserves, so it remains incomplete and is not fully realized.
At the back of his head, Niggle knows that he has a great trip looming, and he must pack and prepare his bags.
Also, Niggle's next door neighbour, a gardener named Parish, is the sort of neighbour who always drops by whining about the help he needs with this and that. Moreover, Parish is lame and has a sick wife, and honestly needs help — Niggle, having a good heart, takes time out to help.
And Niggle has other pressing work duties that require his attention. Then Niggle himself catches a chill doing errands for Parish in the rain.
Eventually, Niggle is forced to take his trip, and cannot get out of it. He has not prepared, and as a result ends up in a kind of institution, in which he must perform menial labour each day.
In time he is paroled from the institution, and he is sent to a place 'for a little gentle treatment'. But he discovers that the new country he is sent to is in fact the country of the Tree and Forest of his great painting, now long abandoned and all but destroyed (except for the one perfect leaf of the title which is placed in the local museum) in the home to which he cannot return — but the Tree here and now in this place is the true realization of his vision, not the flawed and incomplete form of his painting.
Niggle is reunited with his old neighbour, Parish, who now proves his worth as a gardener, and together they make the Tree and Forest even more beautiful. Finally, Niggle journeys farther and deeper into the Forest, and beyond into the great mountains that he only faintly glimpsed in his painting.
But Leaf by Niggle can also be interpreted as an illustration of Tolkien's religious philosophy of creation and sub-creation. In this philosophy, true creation is the exclusive province of God, and those who aspire to creation can only make echoes (good) or mockeries (evil) of truth. The sub-creation of works that echo the true creations of God is one way that mortals honour God.
This philosophy is evident in Tolkien's other works, especially The Silmarillion — one Vala, Morgoth, creates the Orc race as a foul mockery of the elf. Another Vala, Aulë, creates the Dwarf race as an act of subcreation that honoured Eru Ilúvatar (The equivalent of God in Tolkien's writings), and which Eru accepted and made real, just as Niggle's Tree was made real.
Niggle's yearnings after truth and beauty (God's creations) are echoed in his great painting; after death, Niggle is rewarded with the realization (the making-real) of his yearning. Or, if you prefer, Niggle's Tree always existed — he simply echoed it in his art.
From a metanarrative viewpoint, Tolkien's Arda is itself a subcreation designed to honour the true stories of the real world. Thus, the Middle-earth legendarium, despite its lack of overt religious elements, can be interpreted as a profoundly religious work.
An autobiographical interpretation places Tolkien himself as Niggle — in mundane matters as well as spiritual ones. Tolkien was compulsive in his writing, his revision, his desire for perfection in form and in the "reality" of his invented world, its languages, its chronologies, its existence. Like Niggle, Tolkien came to abandon other projects or graft them onto his "Tree," Middle-earth. Like Niggle, Tolkien faced many chores and duties that kept him from the work he loved. And like Niggle, Tolkien was a horrible procrastinator — late in life, he spent hours playing Patience instead of working on The Silmarillion.
Tolkien himself might have disagreed with an allegorical interpretation. He wrote, in Letter 131 of The Letters of J. R. R. Tolkien, "I dislike Allegory." In specific reference to Niggle, he wrote in Letter 241, "It is not really or properly an 'allegory' so much as 'mythical'." On the other hand, in Letter 153 he said, "I tried to show allegorically how [subcreation] might come to be taken up into Creation in some plane in my 'purgatorial' story Leaf by Niggle."