Christians regard the apostles as the connection between the living Jesus, the resurrected Jesus, and the Christian church that developed after Jesus ascended to heaven. The apostles were witnesses to Jesus’ life, recipients of Jesus’ teachings, witnesses to appearances of the resurrected Jesus, and recipients of the wisdom of the Holy Spirit. They were authorities on what Jesus taught, intended, and desired. Many Christian churches today base the authority of religious leaders on their supposed connections to the original apostles.
http://www.whatscatholic.com/the_apostles.html
Classifying apostles tend to be difficult. After the death and resurrection of Christ, there were more than 12. The 11 apostles chose Matthias to replace Judas. In Gal 1:9 we read that James "the Lord's brother" was an apostle. This James should not be confused with James, the son of Zebedee who was also an apostle. So that would be at least thirteen.
Let's not forget the Apostle Paul, who gave us about 80% of the New Testament. Technically, he never saw our Lord Jesus when He walked on earth for 33 years. Although some in the church did not accept him to be an apostle (1 Cor 9:2) most did (certainly Peter who accepted Paul's writings 2 Pet 3:15). And in at least two to three different places we read about people passing themselves off as "false" apostles. This, of course, infers they weren't disguising themselves as one of the twelve but as another apostle. So there must have been far more apostles than we're aware of as the church would accept some as apostles and others as not.
There are indications that not all the apostles were poor or without influence (although all of them sacrificed everything in the end). Peter had a wife and a house. It is believed that John (and thus James) were influential among the higher circles of the Jews since John was "well know" to the high priest. Thus his family must have been well connected. It was John who was admitted entrance into the court of the high priest. It was John and his connections who got Peter into the court where Peter denied Christ. (John 18) Paul, of course, was well off being a Roman citizen and receiving a high education.
In the end, in Revelation 21:14 we read that there are 12 apostles who are the foundation of the church. My guess is they mean Paul, not Matthias.