What is strong-typing versus weak-typing? Which is preferred? Why?

In the most general sense, strong typing means that there are restrictions on the operations that can be performed when objects or values of different types are being intermingled in the same expression or statement. Weak typing means that there are few if any such restrictions.

So, for example, with a weakly typed programming language you may be able to freely intermingle numeric values or numeric strings when creating an expression but in a strongly typed language this sort of thing is severely restricted and usually requires explicit conversions to be made.

The advantage of strong typing is that more errors or potential errors can be picked up at compile time and, knowing the types in advance, the compiler can often produce more efficient code.

The disadvantage of strong typing is that overall development time tends to be longer than with weakly typed languages.

Which type of programming language you prefer is largely a matter of taste but, in my experience, large applications are much easier to manage using a strongly typed language such as C# or C++ whereas small, interactive applications are easier to write using a weakly typed language such as Javascript.