This poem has an element of the confessional about it, as the narrator, the lover of Porphyria that features in the title, recounts to us what happened that evening with Porphyria and looks back on his actions. Interestingly the use of the present perfect tense in the final lines suggests that he is telling us this actually at the scene, whilst he is still with Porphyria:
And thus we sit together now,
And all night long we have not stirred,
And yet God has not said aword!
Maybe we can imagine that he is telling this to some officer or detective to explain the murder. Browning excells in narrative poems that present us with unreliable narrators. By having the narrator tell what has happened to him and his lover from his perspective we are able to see the mind of a deranged murderer at work as he expresses that his act of killing Porphyria was to gain her love eternally:
That moment she was mine, mine, fair,
Perfectly pure and good: I found
A thing to do, and all her hair
In one long yellow string l wound
Three times her little throat around,
And strangled her.
The speaker above all desires and craves possession of Porphyria for himself, and finds the way to gain this by strangling her with her hair, that becomes a "long yellow string" and thus making sure they are united now with no other forces or powers preventing their unity.
Thus the significance of the past tense allows us to analyse the unreliable narrator of this excellent poem and consider his motives and reasons for his actions.