Process-injection is, well, a process by which one process is inspected or manipulated from the inside, by another process.
Process-injection has many use-cases, depending on who you are. For developers specializing in information security, it allows a developer to investigate vulnerabilities that could be exploited by a potential attack. For an attacker, it provides a means of manipulating the memory and sending messages to objects / calling methods on objects, without the host process's knowledge.