This is the sad story of a man who is double suffering: he suffers because he lost his love, and he suffers because she has forgotten him. So even if she is quite alive, her love for him is truly dead. That's why the image of death is slipped into the poem so many times, and we get the correct idea that the pain of the poet is, in fact, a real mourning. Just the tragic atmosphere Romantic poets seemed to cherish: Love/Death, the most important ideas in Romanticism joined together in this masterpiece.

The first four verses state the subject of the poem: the end of love between a man and a woman.

Line 1: "When we two parted"
The reader knows only with the first line that this is a broken-up story, they are not together. We do not know, as readers, why they are not together, maybe because her death, maybe because her love ended. The two of them, lovers before, now are nothing, only words written in a poem.

Line 2: "In silence and tears"
Why silence? It could be because it is a forbidden love and that is the reason why they have to cry in silence. The word "tears" clarify it was a painful loss, they live in tears.

Line 3: "Half-broken hearted"
The word "half" gets our attention, the heart is only half broken, probably because they both new they were doing the right thing and agreed on the separation, or (we’ll find out later) because his heart was broken but her heart wasn't.

Line 4: "To sever for years"
They will be separated for years, but not forever, so maybe deep in his heart he still thinks there is a possibility of getting together again in the future. But that hope is absent in the rest of the poem (which sounds quite definite about the end of this), so his choice of "for years" instead of "forever" is most probably a poetical need, to make this line rhyme with the previous line 2 "in silence and tears" (tears-years).

Lines 5 and 6: "Pale grew thy cheek and cold, colder thy kiss;"
When they two parted her cheek was pale and cold, but her kisses were much colder. These two lines make us think of her death (typical exaggerations of Romanticism poetry). It could mean that she's dead (because her skin turned pale and her lips cold) or that her kisses were cold because she had no feelings about it. We know that she wasn't dead, but the reader doesn't know that yet. The reader thinks "maybe she turned her love away, or maybe she died"; the first thing is true, but the second option got into our head. That way, the poet can transmit to us his vision of the separation: it was as dramatic as death. He felt exactly the same as when the person you love dies and you lose them forever. That was not what happens, but that's how the poet felt it to happen, and the poem is not about facts, it is about feelings. Now, just with the first 6 lines, we're deep inside the tragic feelings of the poet, and we can read the rest of the information knowing exactly how the poem feels about all that.

Lines 7 and 8: "Truly that hour foretold sorrow to this"
That moment, when they parted and she was so cold, was announcing all the suffering the poet would go through in the future about this love affair.

Lines 9 and 10: "The dew of the morning sunk. Chill on my brow"
"Dew" is a romantic feature, a romantic word, a nature element to express the feelings of the author, like rain (=sadness), but colder and more subtle. What does he want to say in this line? The dew in the morning is cold, and wet, a bit as if it had rained during the night. The rain is an allegory of crying, so it means sadness, depressions; the dew is like the feeling we have after crying, less intense but more durable: it gives the idea of melancholy, loneliness.

Lines 11 and 12: "It felt like a warning, of what I feel now"
That pain and loneliness he felt at that moment was an announcement of how he would feel in the future: sad and lonely.

Lines 13 and 14: "Thy vows are all broken, And light is thy fame;"
She was married, broken vows refer to broken promises. When you marry somebody you must be faithful, and she broke her promise having an affair with Byron. But he might also refer to the vows she made to himself: she promised him love but now she changed her mind and decided to abandon him and be faithful to her husband, which, of course, is the right thing to do for her, but breaks the poet's heart. Her light fame means "her luckiness": she's lucky because her husband does not know and now she can continue with her marriage as if nothing had happened, whereas Byron, the poet, is left with nothing.

Lines 15 and 16: "I hear thy name spoken, And share in its shame."
His tone is shameful; he feels the pain of their sin when he hears her name. Every time he hears her name, he remembers they had an illicit relationship and feels shameful about it.

Lines 17 and 18: "They name thee before me, A knell to mine ear;"
Her name is a knell (a bell ring) like a slow sad bell at a funeral death. Again, Byron speaks of this woman as if she was dead, because that's how he feels about this.

Lines 19 and 20: "A shudder comes o'er me- Why wert thou so dear?"
When he hears her name, when he knows about her, a shudder comes over him (all his body trembles with emotion), but why? What power did she have over him?: he loved her too much, and he regrets that because he's suffering for it (why were you so dear? why did I love you so much?= it's not a question, it's a lament)

Lines 21 and 22: "They know not I knew thee, Who knew the too well;-"
The love was totally secret, not even those who know her well knew about this love.

Lines 23 and 24: "Long, long shall I rue thee, Too deeply to tell."
He is regretful for having met her, and too sad to express it. His feeling of regret is so intense that he can't express it with words (too deeply to tell)

Lines 25, 26, 27 and 28: "In secret we met- In silence I grieve, That thy heart could forget, Thy spirit deceive."
He remembers their hidden love encounters and he feels bad because her heart forgot their short but intense love. He can't say anything about this and he can't tell her about this (because he has no contact with her anymore), so he suffers in silence, he can't talk about it. He suffers because she forgot their love and her spirit deceived him (probably by making him think she would love him forever)

Lines 29, 30, 31 and 32: "If I should meet thee, After long years, How should I greet thee? - With silence and tears."
Byron asks himself how he should greet her if he met her again after all these years, which is very improbable ("if I should meet thee"). The answer is "with silence and tears". He would pretend not to know her (as they always did) but he would silently cry in sorrow. This may be because he can't let people know he knows her, or because he thinks he can't talk to her anymore, so it would be useless trying to speak to her since she would pretend she doesn't know him.

This last line is an echo of line 2, so the end of the story mirrors the beginning of it: "silence and tears", that’s the summary of his life since he lost her, it is now, and it will still be the same in the future if they meet again.