A program which executes other programs. This is in contrast to a compiler which does not execute its input program (the "source code") but translates it into executable "machine code" (also called "object code") which is output to a file for later execution. It may be possible to execute the same source code either directly by an interpreter or by compiling it and then executing the machine code produced.
It takes longer to run a program under an interpreter than to run the compiled code but it can take less time to interpret it than the total required to compile and run it. This is especially important when prototyping and testing code when an edit-interpret-debug cycle can often be much shorter than an edit-compile-run-debug cycle.
Interpreting code is slower than running the compiled code because the interpreter must analyse each statement in the program each time it is executed and then perform the desired action whereas the compiled code just performs the action. This run-time analysis is known as "interpretive overhead". Access to variables is also slower in an interpreter because the mapping of identifiers to storage locations must be done repeatedly at run time rather than at compile time.
There are various compromises between the development speed when using an interpreter and the execution speed when using a compiler. Some systems (e.g. some Lisps) allow interpreted and compiled code to call each other and to share variables. This means that once a routine has been tested and debugged under the interpreter it can be compiled and thus benefit from faster execution while other routines are being developed. Many interpreters do not execute the source code as it stands but convert it into some more compact internal form. For example, some BASIC interpreters replace keywords with single byte tokens which can be used to index into a jump table. An interpreter might well use the same lexical analyser and parser as the compiler and then interpret the resulting abstract syntax tree.
There is thus a spectrum of possibilities between interpreting and compiling, depending on the amount of analysis performed before the program is executed. For example Emacs Lisp is compiled to "byte-code" which is a highly compressed and optimised representation of the Lisp source but is not machine code (and therefore not tied to any particular hardware). This "compiled" code is then executed (interpreted) by a byte code interpreter (itself written in C). The compiled code in this case is machine code for a virtual machine which is implemented not in hardware but in the byte-code interpreter.