JPEG compression is considered a lossy compression, because it is not possible to build the exact binary from an original source through uncompression.
Even at the highest quality, JPEG works by discarding data. You control the quality to trade off what you think is an acceptable loss to still have a fair representation of your image. Although data is lost, what can be seen might still be identical to the untrained eye - and that is the point. The same as what minidisc used to do for audio.
The intent for JPEG is to make photographic images smaller in file size for internet transmission, you get to decide how small, but if you want absolute quality a format like TIFF is better suited.
Incidently, TIFF offers a lossless compression, but the file sizes are still massive!
One more thing... If you take a 300 x 500 bitmap and convert it to JPEG, then convert it back. The file size will still be the same, because bitmap works by storing a common number of bits per pixel. But the contents of the file will be quite different. In this regard it might be naively viewed as lossless, but in practical terms it is far from it.