Try this explanation on...
TypeSafe means that variables are statically checked for appropriate assignment at compile time. For example, consder a string or an integer. These two different data types cannot be cross-assigned (ie, you can't assign an integer to a string nor can you assign a string to an integer).
For non-typesafe behavior, consider this:
object x = 89;
int y;
if you attempt to do this:
y = x;
the compiler throws an error that says it can't convert a System.Object to an Integer. You need to do that explicitly. One way would be:
y = Convert.ToInt32( x );
The assignment above is not typesafe. A typesafe assignement is where the types can directly be assigned to each other.
Non typesafe collections abound in ASP.NET (eg, the application, session, and viewstate collections). The good news about these collections is that (minimizing multiple server state management considerations) you can put pretty much any data type in any of the three collections. The bad news: because these collections aren't typesafe, you'll need to cast the values appropriately when you fetch them back out.
For example:
Session[ "x" ] = 34;
works fine. But to assign the integer value back, you'll need to:
int i = Convert.ToInt32( Session[ "x" ] );
Read about generics for ways that facility helps you easily implement typesafe collections.
C# is a typesafe language but watch for articles about C# 4.0; interesting dynamic possibilities loom (is it a good thing that C# is essentially getting Option Strict: Off... we'll see).