Q:

What does it mean that baptism "erases original sin"?

The Catechism of the Catholic Church states regarding original sin:

Human nature has not been totally corrupted: it is wounded in the
  natural powers proper to it, subject to ignorance, suffering and the
  dominion of death, and inclined to sin - an inclination to evil that
  is called "concupiscence". Baptism, by imparting the life of Christ's
  grace, erases original sin and turns a man back towards God, but the
  consequences for nature, weakened and inclined to evil, persist in man
  and summon him to spiritual battle.

So in baptism, original sin is erased, but the nature is still "inclined to evil." What's the difference between a baptized and unbaptized person with regard to their inclination to sin and the state of their nature?

A:

The Church teaches that the human propensity to sin is a result of original sin:

Following St. Paul, the Church has always taught that the overwhelming misery which oppresses men and their inclination toward evil and death cannot be understood apart from their connection with Adam's sin and the fact that he has transmitted to us a sin with which we are all born afflicted, a sin which is the "death of the soul."

(Catechism of the Catholic Church, paragraph 403; emphasis added)
Now as you note, Catholicism holds that baptism removes all sin, both actual and original. In addition to the excerpt you cite from the Catechism, St. Thomas Aquinas in the Summa Theologica states:

As the Apostle says (Rom. 6:3), "all we, who are baptized in Christ Jesus, are baptized in His death." And further on he concludes (Rom. 6:11): "So do you also reckon that you are dead to sin, but alive unto God in Christ Jesus our Lord." Hence it is clear that by Baptism man dies unto the oldness of sin, and begins to live unto the newness of grace. But every sin belongs to the primitive oldness. Consequently every sin is taken away by Baptism.

(Summa Theologica, Third Part, Question 69, Article 1. The Bible quotes in this translation are taken from the Douay-Rheims Bible.)
However, the baptized person is in the same state as the unbaptized with regard to what (as you see in your quote) the Church calls "concupiscence", the desire to put one's own will over God's, and thus to sin. This "concupiscence" is not identical with original sin, but is inherited as a consequence of the original sin. Thus, even with baptism when the original sin is washed away, the consequences are not:

By Baptism He takes away from man forthwith the guilt of original sin and the punishment of being deprived of the heavenly vision. But the penalties of the present life, such as death, hunger, thirst, and the like, pertain to the nature, from the principles of which they arise, inasmuch as it is deprived of original justice.

(Summa Theologica, Third Part, Question 69, Article 3, ad 3)
In other words, we were created to live in God's justice ("original justice"); but the sin of Adam and Eve—the original sin—permanently removed all their descendants from that state by changing the nature of human beings, and consequently we are inevitably prone to actual sin, even when the guilt of original sin (and any prior sins we may have committed) has been washed away in Baptism.

A:

Roman Catholicism teaches that water baptism done in the name of the Trinity washes away all kinds of sins.This means that a baptized person is cleansed from all sins. There is 0% sin in the baptized person.They use the following Bible verses to support this teaching: 

Acts 22:16 (NIV)
16 And now what are you waiting for? Get up, be baptized and wash your
  sins away, calling on his name.’
1 Peter 3:20-21 (NIV)
20 to those who were disobedient long ago when God waited patiently in
  the days of Noah while the ark was being built. In it only a few
  people, eight in all, were saved through water, 21 and this water
  symbolizes baptism that now saves you also—not the removal of dirt
  from the body but the pledge of a clear conscience toward God.[a] It
  saves you by the resurrection of Jesus Christ,
Romans 6:22 But now that you have been set free from sin and have
  become slaves of God, the benefit you reap leads to holiness, and the
  result is eternal life.

The baptized is in the state of 0% sin due to the new birth ( water baptism). This state of sinlessness is the same state of Adam and Eve pre-fall.This is why the baptized is called a "new creature" ( 2 Corinthians 5:17)  
This means that the baptized is able to freely choose either to sin ( personal sin: venial or mortal) or not to sin ( continue in the state of sanctifying grace).
If the baptized commited mortal sin ( and died without forgiveness), he'll be doomed to hell. If the baptized commited venial sin ( and died), purgatory ( final sanctification) will be undergone and after satisfying temporal punishment, heaven is the sure destination.
In other words, Roman Catholicism teaches that upon the forgiveness of the original sin by baptism, the baptized received sanctifying grace wherein he will continue ''to work out his salvation with fear and trembling'' (Philippians 2:12). Now when a baptized person sinned a mortal sin, actual grace is given by God. Actual grace is a call to the soul to repent and come back to follow God again in the state of sanctifying grace. 
Reference: 
http://www.catholic.com/tracts/the-forgiveness-of-sins
http://www.catholicculture.org/culture/library/catechism/index.cfm?recnum=4104 
http://www.catholic.com/magazine/articles/baptism-saves-you

