The poem is built around a major juxtaposition: that between the old and the young. At the same time, the poem makes it clear that the gap between those seemingly distinct groups isn't really all that wide.
The poem's first stanza focuses on the exuberance of the children playing and of the natural world in spring. Everything, from the sun to the skies to the birds, seems full of energy. The children's "sports" go on "while" the world rejoices around them.
In the next stanza, the poem turns to the elderly folks who watch the children at play. Whereas the children are up and running about, these "old folk" sit under an oak tree and reminisce. That oak tree itself symbolizes longevity and maturity, and its presence speaks to the fact that people like "Old John" are in a much different stage of life.
And yet, it's also clear that the "old folk" see the kids as a reflection of their younger selves: these kids are doing exactly what the old people used to do when they were "girls & boys." Even as the poem juxtaposes these groups, then, there's also a sense of continuity here: those kids will one day be sitting under the oak tree, watching a new generation play on the green.
In other words, juxtaposition helps to make this poem's central point: change is life's constant, and everything that lives is part of the same "ecchoing" natural cycle of life, death, and rebirth.