The key sense used in this poem is sound. The "poetry of the earth" refers to the many different sounds in nature. When the birds are too hot from the sun, cooling in the trees, one can hear the "voice" or sound of the grasshopper. Likewise, when the grasshopper is resting or inactive (and therefore making no sounds: no poetry), the cricket can be heard. In each case, it is as if when one creature takes a rest, another becomes active: as if collectively, these creatures were taking turns reading "the poetry of the earth."
In the last two lines, the author gives the impression that the birds, the grasshopper, and the cricket are all singing the same song, all reading the same poem.
The Cricket's song, in warmth increasing ever,
And seems to one in drowsiness half lost,
The Grasshopper's among some grassy hills.
That is to say, to one (a person) who is half asleep, he might think that the Cricket's song is the Grasshopper's. This supports the idea that the Cricket and the Grasshopper are singing/reciting the same poetry of the earth. To one who is half drowsy, their songs/poems might sound similar. This poem, and many of Keats' poems, deals with the relationship between art (poetry) and nature.