If you're new to design, or simply have been given some files to work with, which ones are used for which purpose? Here follows a very brief post attempting to simplify a very large subject.
Files with an .indd suffix are created in InDesign, which is the program most widely used to create documents that will be printed, such as magazines, newspapers, brochures and newsletters. It's this file that you'd open in InDesign if you wanted to change any aspect of the file that you've been sent.
Images that are placed within the InDesign file usually come from two different sources. Some are most likely photographs, usually created in Photoshop, and will very often be .jpg files. Other file types created from Photoshop include the .tiff file and the .psd.
What all of these file types have in common is that they are images made out of pixels (also called bitmap or raster images, because they've been rasterised: converted into pixels). What separates them are their different attributes. Jpgs are very effective at compressing images in the same way that mp3 files compress audio files to make them smaller. Tiffs compress in a less effective way, but do so without throwing away any information from the image, so are often regarded as being of higher quality (which is not necessarily true). PSD files are Photoshop's native file format and enable you to use some of Photoshop's very flexible features (like Layer Masks, Smart Objects, Smart Filters). Other bitmap file formats that are primarily used for web graphics (as well as jpgs) are the .gif and the .png file format. Mostly you wouldn't need to open bitmap images, but would do so in Photoshop if you wanted to change the images (for example to make it black and white, or adjust its colours).
The other source for images that are placed within Indesign is Illustrator, which creates images not make out of pixels, but mathematically determined points called vectors. These files are much simpler than bitmap images and are perfect for things like logos, diagrams and maps. The files created from Illustrator are usually .ai files and .eps files. Again, you normally shouldn't need to open these, but you would do so in Illustrator if you wanted to adjust the colours in a logo or change the text on a diagram.
The other file type you'll have come across is the pdf, which can be created by a variety of programs for a variety of reasons. The most likely reason you'd encounter one in a design context is that it is either sent as a proof (so you can see how the job will print out) or that it's created as the final document for a printer to print from.
If you're completely new to the world of design and have no idea where to start, take a look at our sister site, The Accidental Designer.