A dynamic programming language is a programming language in which operations otherwise done at compile-time can be done at run-time. For example, in JavaScript it is possible to change the type of a variable or add new properties or methods to an object while the program is running.
This is opposed to so-called static programming languages, in which such changes are normally not possible.
Note that while there is indeed a connection between this dynamic/static property of programming languages and dynamic/static-typing, the two are far from synonymous.
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- Dynamic programming language on Wikipedia