Purple is the team that combines both offensive and defensive testing techniques to protect an organization's critical systems. Purple is not a separate team, but rather a collaboration between the red team and the blue team. The red team is the offensive team that simulates attacks and exploits vulnerabilities in the organization' s systems. The blue team is the defensive team that monitors and protects the organization's systems from real and simulated threats. The purple team exists to ensure and maximize the effectiveness of the red and blue teams by integrating the defensive tactics and controls from the blue team with the threats and vulnerabilities found by the red team into a single narrative that improves the overall security posture of the organization.
Red, blue, and yellow are other types of teams involved in security testing, but they do not combine both offensive and defensive techniques. The yellow team is the team that builds software solutions, scripts, and other programs that the blue team uses in the security testing. References: CompTIA Security+ Study Guide:
Exam SY0-701, 9th Edition, page 1331; Penetration Testing: Understanding Red, Blue, & Purple Teams3

A buffer overflow is a vulnerability that occurs when an application writes more data to a memory buffer than it can hold, causing the excess data to overwrite adjacent memory locations. A register is a small storage area in the CPU that holds temporary data or instructions. An attacker can exploit a buffer overflow to overwrite a register with a malicious address that points to a shellcode, which is a piece of code that gives the attacker control over the system. By doing so, the attacker can bypass the normal execution flow of the application and execute arbitrary commands.