Type safety is an attribute that some programming languages have. It is a way of preventing a set of possible programming errors by making the compiler more aware of what you are doing, so it is aware of what you are doing wrong.
The gist of it is that in a type safe language, you use the type system of that language to express to the system what the valid operations are. If you then attempt an invalid operation, then the compiler can reject it rather than just executing it blindly and getting a random output.
There are three types of language with respect to type safety: DynamicallyTypedLanguages, StaticallyTypedLanguages, and UntypedLanguages.