Browning's 'Porphyria's Lover' is a dramatic monologue which means it is written in the first person allowing us to see into the mind of the speaker. Clearly as the speaker is a murderer this is interesting to us as it allows us to see his motivation.
It appears that Porphria is attached to another; 'vainer ties dissever' and the speaker is jealous of this and wants to keep her to himself; the only way he can do this is to kill her so she cannot leave. The killing does not appear to be planned; in fact it is chillingly casual 'I found/A thing to do' and the speaker does not seem to feel any remorse or guilt. He feels that he has got away with it; 'And yet God has not said a word!' He has attemped to 'freeze' a perfect moment and has done so.