"Lossy" refers to lossy compression. The most significant format using this is JPEG.
Lossy compression is a slight misnomer. What actually happens in JPEG conversion is that the data is slightly modified to facilitate better compression. The actual compression of the modified data is not, itself, lossy ( typically it's Huffman encoding ).
The modifications to the data are designed to be visually least significant. Even zoomed in it can be quite hard to spot the subtle difference between an uncompressed original and a very compressed JPEG.
The thought of using "lossy" formats tends to petrify some amateurs ( and the occasional pro ), but it really isn't a significant issue for any expect the most extreme pixel peepers.
There is a lossless version of JPEG ( called JPEG2000 ), but this is not widely used outside the medical and some scientific professions ( where any loss is unacceptable ). Unfortunately cameras and mobile devices and most software do not generally support JPEG2000.