Type-safe means that the set of values that may be assigned to a program variable must fit well-defined and testable criteria. Type-safe variables lead to more robust programs because the algorithms that manipulate the variables can trust that the variable will only take one of a well-defined set of values. Keeping this trust ensures the integrity and quality of the data and the program.
For many variables, the set of values that may be assigned to a variable is defined at the time the program is written. For example, a variable called "colour" may be allowed to take on the values "red", "green", or "blue" and never any other values. For other variables those criteria may change at run-time. For example, a variable called "colour" may only be allowed to take on values in the "name" column of a "Colours" table in a relational database, where "red, "green", and "blue", are three values for "name" in the "Colours" table, but some other part of the computer program may be able to add to that list while the program is running, and the variable can take on the new values after they are added to the Colours table.
Many type-safe languages give the illusion of "type-safety" by insisting on strictly defining types for variables and only allowing a variable to be assigned values of the same "type". There are a couple of problems with this approach. For example, a program may have a variable "yearOfBirth" which is the year a person was born, and it is tempting to type-cast it as a short integer. However, it is not a short integer. This year, it is a number that is less than 2009 and greater than -10000. However, this set grows by 1 every year as the program runs. Making this a "short int" is not adequate. What is needed to make this variable type-safe is a run-time validation function that ensures that the number is always greater than -10000 and less than the next calendar year. There is no compiler that can enforce such criteria because these criteria are always unique characteristics of the problem domain.
Languages that use dynamic typing (or duck-typing, or manifest typing) such as Perl, Python, Ruby, SQLite, and Lua don't have the notion of typed variables. This forces the programmer to write a run-time validation routine for every variable to ensure that it is correct, or endure the consequences of unexplained run-time exceptions. In my experience, programmers in statically typed languages such as C, C++, Java, and C# are often lulled into thinking that statically defined types is all they need to do to get the benefits of type-safety. This is simply not true for many useful computer programs, and it is hard to predict if it is true for any particular computer program.
The long & the short.... Do you want type-safety? If so, then write run-time functions to ensure that when a variable is assigned a value, it conforms to well-defined criteria. The down-side is that it makes domain analysis really difficult for most computer programs because you have to explicitly define the criteria for each program variable.