The shell is the program which actually processes commands and returns output. Most shells also manage foreground and background processes, command history and command line editing. These features (and many more) are standard in bash, the most common shell in modern linux systems.
A terminal refers to a wrapper program which runs a shell. Decades ago, this was a physical device consisting of little more than a monitor and keyboard. As unix/linux systems added better multiprocessing and windowing systems, this terminal concept was abstracted into software. Now you have programs such as Gnome Terminal which launches a window in a Gnome windowing environment which will run a shell into which you can enter commands.
The console is a special sort of terminal. Historically, the console was a single keyboard and monitor plugged into a dedicated serial console port on a computer used for direct communication at a low level with the operating system. Modern linux systems provide virtual consoles. These are accessed through key combinations (e.g. Alt+F1 or Ctrl+Alt+F1; the function key numbers different consoles) which are handled at low levels of the linux operating system -- this means that there is no special service which needs to be installed and configured to run. Interacting with the console is also done using a shell program.
