Often these verses are interpreted to talk about what happens when either someone repents of their sins or is delivered of an evil spirit. It is important after that has happened to fully accept Jesus Christ, that is to acknowledge him as Lord. And it is important to be filled with the Holy Spirit, to yield every part of you to him so that evil spirits can't move in. This is a good interpretation but there is a prophetic and eschatological meaning also. And I would contend that it was this meaning - prophecy of times to come - that was in the forefront of the minds of those who first heard Jesus preaching this parable.
Seeing these verses as a prophecy of judgement on Israel and Jerusalem in particular, we can interpret it like this: Jesus Christ swept clean Jerusalem by casting out demons and proclaiming the truth about himself and God the father. He told the parable about this.
The house was swept clean and put in order but because many of the house of Israel him, the blessings they had received would turn into curses. Jerusalem had been “swept clean” by Christ’s ministry and so now it was a great place for spirit to take up residence. This prophecy by Jesus did indeed come to pass as alluded to in Revelation.
What Jesus did next was to order from his position in heaven the destruction of Jerusalem.
The application for today of this prophetic interpretation of these verses:
When a society tries to clean up its act morally and ethically it is doomed to failure without the Holy Spirit. Especially when, as with that generation of Jews at the time of Jesus, many in a country today have had the opportunity to accept Jesus. And when that nation has had Christianity as part of its culture and rejected Christianity, just as Israel had the Scriptures and the Prophets and the Temple and rejected Jesus' authority: Judgement will fall.