Browning is perhaps best known for a series of poetic dramatic monologues, in which he speaks through various characters. Some of the most famous examples of those include "My Last Duchess" and "Porphyria's Lover."
Still, "Home-Thoughts, from Abroad" is more in keeping with another strain in Browning's work: the travel poem. Clearly his time in Italy left an impression on him, as poems like this and "Home-Thoughts, from the Sea" reflect.
Of course, Browning was a good enough poet that he was able wrap his travel experiences inside one of his dramatic monologues. Check out "The Italian in England" to see what that's all about. It's like he's mixed chocolate and peanut butter and came out with a poetic Reese's cup.