Lossy and Lossless Compression

An image file type can either be lossy or lossless. This determines the kind of quality the image will be when it is saved or edited.

Lossless Compression

Lossless compression means that when a file is compressed, it will not lose any quality. It allows for large, high quality images to be saved and compressed, and have a smaller file size but retain their quality. Examples of file types that use this kind of compression are GIFS and PNG, which are commonly used across the internet for their ability to be shared easier than other image file types and still be good quality. The technique used to compress images in lossless compression essentially rewrites the information contained in the file more efficiently, and although the resulting file is smaller, it is not as small as a file produced by lossy compression. This type of file type is good for things such as concept art and graphic design where images or often manipulated.
http://searchcio-midmarket.techtarget.com/definition/lossless-and-lossy-compression

Lossy Compression

Lossy compression works by erasing redundant information in an image file and therefore permanently reducing the file size. This results in a smaller file than if lossless compression were used however there is much more of a decline in quality (Although it is not noticeable when the image has only been saved or edited once or twice). This is especially noticeable when the image has been saved many times, as the image will lose more quality each time it is saved making it look "blockier" and more "pixelated" every time. However file types such as JPEGs have a Quality Settings feature where, upon saving the image, one can chose how much they want the image to be compressed. For example, a highly compressed image would take up very little disk space but may not look as good as the original. This is useful for sharing images online.
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To compare the two; lossy compression offers smaller file sizes that take up less disk space and are easy to send over the internet however the image quality is very low. Lossless compression allows for very high quality images due to it's advanced compression technique, however it produces larger file sizes than lossy compression would meaning more disk space is taken up.

The picture below shows the different between a PNG file which uses Lossless compression, and a JPEG using Lossy compression;

http://images.sixrevisions.com/2010/11/17-02_lossy_lossless.jpg