"On This Day I Complete My Thirty-Sixth Year" begins with a sudden declaration: "'Tis time this heart should be unmoved, / Since others it has ceased to move." Alongside the poem's title, this first line gives the reader a sense that the speaker feels he's moving into a new epoch of his life. Something big is changing.
That big change seems to be both to do with age and with love. This speaker can no longer "move" other hearts: no one, he believes, is going to love him back anymore. To a modern-day reader, the idea of being too old for love at 36 sounds a little silly, but this speaker seems deadly serious: this is a big enough deal that he needs to write a poem to commemorate his life change. (Indeed, this is likely an autobiographical poem; its author, Lord Byron, was a major celebrity and heartbreaker in his day, and as such he might well have felt washed-up as he moved out of full-blown youth. More on that in the "Context" section.)
But this brooding speaker isn't giving up on love altogether. Rather, he's renouncing being loved back. Take a look at the parallel structure in these first lines:
'Tis time this heart should be unmoved,
Since others it hath ceased to move:
Yet though I cannot be beloved,
Still let me love!
This stanza is all one sentence, and its grammatical structure reflects back over itself across the central colon. The speaker also uses polyptoton here, repeating the related words "unmoved" and "move," "beloved" and "love." These repetitions, the same gist but slightly different, suggest that this speaker is moving not away from love completely, but into a different experience of love. He may not be loved back, but he longs to go on loving anyway.
The ABAB rhyme scheme here also supports this idea of an evolving perspective on love. All the end rhymes here are slant, almost matches, but not perfect ones. Again, this reflects the speaker's new experience of love: he's no longer going to find a lover who can provide a perfect match, a perfect rhyme, for his feelings.
This speaker, reaching middle age, thus prepares to renounce an old life, but also to accept—and even embrace—a new one.