Short answers, pulled from the story.
The Twin Towers were Tim Duncan and David Robinson, the two starting centers who played together for the San Antonio Spurs from 1997 to 2003. Both were selected first overall in the NBA draft by the Spurs, Robinson in 1987 and Duncan in 1997, and both spent their entire careers with San Antonio.
The Twin Towers won two NBA championships, in 1999 and 2003. In 1999 they defeated the New York Knicks, and in 2003 they defeated the New Jersey Nets in Game 6, with Robinson recording 13 points and 17 rebounds in his final NBA game.
Robinson was selected first overall in the 1987 NBA Draft but had an active-duty military obligation with the Navy that prevented him from joining the Spurs for two years. He began college at Navy with no expectation of playing in the NBA.
During the Twin Towers era, Tim Duncan was named NBA Rookie of the Year, was selected to the All-NBA First Team and the All-Star Game in his rookie season, won NBA MVP awards for the 2001-02 and 2002-03 seasons, and was named NBA Finals MVP in both 1999 and 2003. He and Robinson were jointly named Sports Illustrated's Sportsmen of the Year in 2003.
After finishing with the third-worst record in the 1996-97 season, the Spurs won the NBA draft lottery, giving them the first overall pick in the 1997 NBA Draft. They used that pick to select Tim Duncan from Wake Forest.
Robinson retired after the 2002-03 season, his final game being Game 6 of the 2003 NBA Finals. The Spurs retired his number 50 jersey on the 10th of November 2003, and he was inducted into the Naismith Memorial Basketball Hall of Fame in 2009 in his first year of eligibility.