What is the context of Byron's "When We Two Parted"?

The context of Byron's "When We Two Parted" is the dissolution of a relationship between two people.
It is not difficult to imagine Byron writing this poem from a personalized context. Byron had many affairs and experienced many relationships begin and end. As a result, the poem's context is the disintegration of a love affair. 
While Byron writes from personal experience, the way he constructs the poem's emotional landscape makes it relatable to anyone who has fallen in and out of love. For example, the context of the first two stanzas is a dying relationship. What used to be love and passion is now shrouded in "silence and tears." Byron skillfully suggests that relationships do not die when two people leave. Rather, there are elements that show emotional distance before the actual breakup. He communicates this dynamic in lines like "half broken-hearted/ To sever for years." Byron's imagery of "pale grew thy cheek" and "Colder thy kiss" suggests people part begin to part before they actually do. Byron speaks of "the warning" signs that show a relationship has run its course. These markers indicate love's death. They take place when "vows are all broken" and when a person's name illuminates "shame" where love once was.
The context of regret is illuminated in the final two stanzas. Byron experiences "a shudder" to the question of "Why wert thou so dear?" The questioning of why or how we could have loved someone is another stage of the process of love dying. Realizing this does not bring happiness, but rather "rue." It is a "silence" that accompanies how we "grieve" when someone so positive is now the source of so much hurt. Byron suggests there are no winners when love dies. The poem's closing context is a mourning and cavernous remorse at what once was.
The highly emotional context of "When We Two Parted" is part of its effectiveness. Its primacy on personal experience is what makes it Romantic. Byron's own personal context is able to generate an emotional field we walk through, surveying his pain and our own.