To me, this verse is about repentance. Every day repentance.
Every day we sin by what we do and by what we fail to do. The only way we can empty ourself of today's sin is to get down on our knees, confess our daily sins, and ask for the mercy of God through Jesus the Son.
When we ask for mercy through Jesus, we are saying our spirit is broken. When we empty our spirit of pride and self-sufficiency, we are poor in spirit. Our spirit is broke, our spirit is penniless, our spirit is nothing. And that is what God wants from us, a contrite spirit turning to Him, acknowledging the poverty of our spirit.
Then we look around and we see we are in the Kingdom of Heaven, the dwelling place of the saved. We never really left the Kingdom from the day before, from the last time we were on our knees asking for mercy. But, somehow, we forgot about the Kingdom, we busied our spirit with things of this world, we fell into sin again by what we did and by what we failed to do in the course of the day.
And now, on our knees, in our poverty, we receive the mercy of God through Jesus the Son, the sins of the day are forgiven, we are washed clean, and the Holy Spirit fills us up so we can see the terrain of the Kingdom of Heaven once again. The Holy Spirit is strong and takes control of our spirit. We feel the Kingdom around us and we know it is real.
And soon, sooner that it should ever be, we open our eyes, rise from our knees, and the terrain of this world takes shape again, in some way we do not understand, and we start again to do what we should not do and we fail to do what we should do--until we are on our knees again.
That is what Matthew 5:3 means to me.
...Bob