(edit: the following applies to C# and similar, strongly-typed programming languages. I'm not sure if this helps you).
For example, the following error will be detected by the compiler (at compile time) before you run a program and will result in a compilation error:
int i = "string"; --> error at compile-time
On the other hand, an error like the following can not be detected by the compiler. You will receive an error/exception at run-time (when the program is run).
Hashtable ht = new Hashtable();
ht.Add("key", "string");
// the compiler does not know what is stored in the hashtable
// under the key "key"
int i = (int)ht["key"]; // --> exception at run-time