Let's look at the poem verse by verse. For a Hughes poem, it is surprisingly literal.
The Laburnum top is silent, quite still
In the afternoon yellow September sunlight,
A few leaves yellowing, all its seeds fallen.
The poet describes a Laburnum tree. It is still on an autumn afternoon, the leaves getting ready to fall.
Till the goldfinch comes, with a twitching chirrup
A suddenness, a startlement, at a branch end.
Then sleek as a lizard, and alert, and abrupt,
She enters the thickness, and a machine starts up
A small bird, a goldfinch, arrives at the tree. The poet uses unfamiliar terms such as "suddenness" and "startlement" to jar the reader's comprehension, just as the frenetic activity of the bird contrasts with the still tree. The bird goes into the foliage of the tree, and there is further commotion described via the metaphor of a machine starting.
Of chitterings, and a tremor of wings, and trillings —
The whole tree trembles and thrills.
It is the engine of her family.
She stokes it full, then flirts out to a branch-end
Showing her barred face identity mask
The commotion continues, shaking the whole tree. Continuing the machine metaphor, the poet casts the baby goldfinches in the tree as "the engine": they are clamouring for food as their mother has come to feed them. Her giving them food to eat until they are satiated is - again with the machine metaphor - described as stoking the engine full. She flies out, stopping to look directly at the poet with her "barred face": the patterns on her plumage.
Then with eerie delicate whistle-chirrup whisperings
She launches away, towards the infinite
And the laburnum subsides to empty.
The bird makes a brief, quiet noise and then flies away - the hugeness of the sky and the possibilities of flight are summaried as "the infinite". The tree is silent and still once more: "empty" in the parlance of the engine.
The purpose of this poem is to highlight the importance of relationships between different species in nature. The bird uses the tree as shelter for her family and without her presence the tree seems lifeless and barren, especially to human eyes. The opening of the poem with its autumnal overtones makes us think of the bare branches, empty of leaves.
The way the stanzas break into three parts highlight this relationship. The first stanza uses long, languid words and describes the still tree. The second uses shorter, sharper sounding words to communicate the quick, flurrying activity of the bird. Then it goes back to the quieter more reflective language for the third, after the bird has left.