What does self righteousness mean?

It means to consider oneself righteous ("as one should be") as measured by a self-imposed, self-determined standard.

Self-righteous people compare themselves to other people in order to see themselves as superior, reasoning along the lines of, "Well, at least I don't (fill-in-the-blank sin) like Mr. Soandso does." Because of this attitude, they also tend to "toot their own horn."

A tremendous example of self-righteousness is found in Luke 18:11, 12 - The Pharisee stood and prayed thus with himself, 'God, I thank You that I am not like other men-extortioners, unjust, adulterers, or even as this tax collector. I fast twice a week; I give tithes of all that I possess.'

On the surface, it seems good for the Pharisee to express thanks to God, but Jesus' teaching goes beneath the surface to reveal that his standard was flawed. Jesus compares the attitude of the Pharisee to that of a tax collector in verse 13 - And the tax collector, standing afar off, would not so much as raise his eyes to heaven, but beat his breast, saying, 'God, be merciful to me a sinner!'

The tax collector's attitude demonstrates the exact opposite of self-righteousness, and Jesus concludes the lesson by pronouncing, in verse 14: "I tell you, this man went down to his house justified rather than the other; for everyone who exalts himself will be humbled, and he who humbles himself will be exalted."

[Quotes from NKJV]