Lossy compression vs lossless compression is the difference of whether you can get a 1:1 copy of the original data if you compress and then decompress it.

A simple example of this is if you have 4 bits of data and have a compression algorithm that turns it into 2 bits of data. If your dataset only contains 0000, 0011, 1100, and 1111; then this can technically be considered lossless compression because we can always reconstruct the exact original data (e.g. 0011 compresses to 01 and can decompress back to 0011, 1100 compresses to 10 and can decompress back to 1100, etc). However, if our dataset later included 1101 and got compressed to 10, this is now “lossy” because it would decompress to 1100, that last bit was “lost”.

An LLM is lossy compression because it lacks the capacity to 1:1 replicate all its input data 100% of the time. It can get quite close in some cases, sure, but it is not perfect every time. So it is considered “lossy”.