A successful two-pointer in basketball is defined by the player shooting the ball from within the three-point line and making a basket. The objective is to score points by successfully navigating the defense and executing a shot that goes through the hoop. Timing, accuracy, and the player's ability to read the game are critical for executing a successful two-pointer. This type of scoring helps teams accumulate points and gain momentum during the game, contributing to overall success in a basketball match.