Runtime is when a program is running (or being executable). That is, when you start a program running in a computer, it is runtime for that program. In some programming languages, certain reusable programs or "routines" are built and packaged as a "runtime library." These routines can be linked to and used by any program when it is running.
Programmers sometimes distinguish between what gets embedded in a program when it is compiler and what gets embedded or used at runtime. The former is sometimes called "compile time."
For a number of years, technical writers resisted "runtime" as a term, insisting that something like "when a program is run" would obviate the need for a special term. Gradually, the term crept into general usage.