.GIF
A .gif is a image file that supports both static and animated images. you should use .gif if you're making a small animated file. 
.JPEG
A .jpeg is a format of a compressed image file which is used for images online and shouldn't be used if you want to print a image.
.PNG
A .png is also known as a portable network graphic, its a format that supports lossless data compression you can use .png to print an image and can change the size of the image without it losing its resolution . 
.PSD
A .psd file is . layered image file used in Adobe photoShop, it allows you to work with the individual layers even after its been saved. 
.TIF
A .tif is a image format file for storing raster graphic images, it can be saved in a variety of colour formats and in various forms of compression.