A friend of mine has asked me today what the difference between compiled and interpreted languages is; so here is the answer for her and anybody else who needs it.
A compiled language is one where you have to compile the code before it can be executed. The compilation process, for those that don't know it, transforms the source code into object code; the later can be directly executed by the microprocessor (as it's formed by opcodes), while the former can't. So, more generically, a compiled language can be executed, after compilation, without any helper utility. Examples of these include C, C++ and assembler.
An interpreted language is one where you can execute the code without compilation, by means of an interpreter. An interpreter reads the code from the source file and executes it, without converting it to machine code (forget about JIT compilers for now). The way this is done depends on the specific interpreter you are using; but to get an idea, they often construct a parse tree - an in-memory representation of the code structure - from the source file and then evaluate it. Examples of these include Perl, Python, PHP, Basic and POSIX shell scripting.
So... where do Java and C# lay? You will get different answers from different people. But, in my opinion, they are interpreted languages. Yes, you have to compile them, but the code you get - bytecode - is not directly executable by the machine: you need an interpreter that runs it afterwards, which IMHO, makes them interpreted. If someone designs a microprocessor that runs Java natively (which is theorically possible, IIRC), this could change.
And at last, let's see what JIT compilers are. JIT stands for Just-In-Time compiler; they are used in interpreters (specially, in Java VMs) to improve runtime performance. How? They convert the original bytecode to native instructions before executing them, so that they can take full profit of the underlying architecture. Note that this process is completely transparent to the developer and to the user, and only depends on the specific interpreter you are using.