To understand linkers, it helps to first understand what happens "under the hood" when you convert a source file (such as a C or C++ file) into an executable file (a file that can be executed on your machine or someone else's machine running the same architecture).
Under the hood, when a program is compiled, the compiler converts the source file into object byte code. This byte code (sometimes called object code) is mnemonic instructions that only your computer architecture understands. Traditionally, these files have an .OBJ extension.
After the object file is created, the linker comes into play. More often then not, a real program that does anything useful will need to reference other files. In C, for example, a simple program to print your name to the screen would consist of:
printf("Hello Nick!\n");
When the compiler compiled your program into an obj file, it simply put a reference to the printf function. The linker resolves this reference. Most programming languages have a standard library of routines to cover the basic stuff expected from that language. The linker links your OBJ file with this standard library. The linker can also link your OBJ file with other OBJ files. You can create other OBJ files that have functions that can be called by another OBJ file. The linker works, almost like a word processor's copy and paste. It "copies" out all the necessary functions your program references and creates a single executable.
Note that not all operating systems create a single executable. Windows, for examples, uses DLL's that keep all these functions together in a single file. This reduces the size of your executable, but makes your executable dependant on these specific DLLs. DOS used to use things called Overlays (.OVL files). This had many purposes, but one was to keep commonly used functions together in 1 file (another purpose it served, in case you're wondering, was to be able to fit large programs into memory. DOS has a limitation in memory and overlays could be "unloaded" from memory and other overlays could be "loaded" on top of that memory, hence the name, "overlays"). Linux has shared libraries, which is basically the same idea as DLL's (hard core linux guys I know would tell me there are MANY BIG differences).
Hope this helps!