Their first reaction is a mixed one. Although they like what he says, they aren't sure why he has said them. They seem to be reluctant to accept that someone that they know could accomplish great things.
Jesus responds by saying that no prophet is accepted in his own hometown.
He then reminds them that both Elijah and Elisha had gone far from home to accomplish miracles. "Many widows in Israel were hungry yet Elijah helped a foreigner. Many lepers were in Israel, but Elisha healed a foreigner." Note they weren't just foreigners, they were not of the same religion as Elijah and Elisha.
We're left to ponder whether the people in Nazareth were blocking Jesus' work among them by their own refusal to accept him as anointed by the Lord--or, whether, Luke is reminding us that God is not restricted to helping hometown folks, that God's power extends beyond the circle of believers.