Blotting out the handwriting of ordinances that was against us, which was contrary to us, and took it out of the way, nailing it to his cross;
Note 16 at Col 2:14: In Paul's day, paper and ink were used when writing. The paper was different, and the ink did not contain acids allowing it to soak into the paper, like it does today. Therefore, the ink could be blotted away so that the writing was illegible or even totally removed. This is what Paul was referring to.
The Old Testament Law has been blotted out. Notice that it is not just our transgressions of the Law that were removed but the ordinances themselves. Jesus took the Law as a document and nailed it to His cross, in effect writing across the bill "Paid in Full." The New Testament believer is no longer under the Law (see note 10 at 1Co 9:21, note 1 at 1Co 10:23, and notes 3-4 at Ro 3:19).
Note 17 at Col 2:14: Notice that Paul was speaking of the Law as being against us and contrary to us. This is radically different than what many Christians think. They embrace the Old Testament Law as something that God gave us for our benefit, to help direct us toward right standing with God. That's not the case.
The O.T. Law was given to show us our sin (see note 4 at Ro 3:19), not our Savior. The Law was condemning (see note 1 at 2Co 3:7), and it empowered sin in our lives (see note 26 at 1Co 15:56, note 5 at Ro 7:11, note 6 at Ro 7:13, and note 7 at Ro 7:14).
Note 18 at Col 2:14: Notice in Paul's analogy that the Law was not totally destroyed; it was just taken out of the way. It is only out of the way of those who are believers in Christ. Those who have not put their faith in Christ are still under the Law (see note 4 at Joh 3:36) with its wrath and negative effects.