Children say this while plucking the petals from a flower, like a daisy, or else while counting the seeds in an apple. The idea is that wherever in the rhyme you end counting petals or seeds (i.e. because you've counted them all) that's what will happen in the future. So if you end on "eight they both love", then the person you're asking about will love you and you will love him.
Growing up in New York in the 70's we would pluck the leaves of daisies or other flowers with the chant ,"He loves me, he loves me not, he loves me, he loves me not, and so on" with the same idea in mind – depending on where you ended plucking you'd know if the boy loved you or not.
One, he loves; two, he loves;
Three, he loves, they say;
Four, he loves with all his heart;
Five, he casts away.
Six, he loves; seven, she loves;
Eight, they both love.
Nine, he comes; ten, he tarries;
Eleven, he courts; twelve, he marries.
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This rhyme can be found in The Real Mother Goose (1916), illustrated by Blanche Fisher Wright. The illustration is from The Little Mother Goose (1912), illustrated by Jessie Willcox Smith.
