MP3 is the 'colloquial' name for "MPEG 1 Layer 3" audio encoding. The purpose of mp3 encoding is to reduce the overall size of an audio data stream whilst maintaining an acceptable level of listening quality.
It is implemented using a "codec", meaning that you need an "Encoding" function and a "Decoding" function in order to listen to the audio. The Encoding device might be hardware or software and the decoding function the same - it might be software or a hardware device.
The entire implementation methodology of mp3 is as a 'lossy' encoding format. "lossy" means that the encoder will remove audio data that it determines is not necessary for that "acceptable quality" level to be maintained. The emphasis here is on "lossy". You lose data when encoding to mp3.
When you decode from mp3 back to a PCM format (such as WAV), that data is gone. It is never coming back.
mp3 can be encoded to a chosen bitrate. The higher the bitrate, the better the overall quality. Also, different types of music behave differently under mp3. Rock music or EDM can be encoded to low bitrates with subjectively lower quality loss than classical music. The waveform generated by a strings instrument is of such complexity that it is very hard to encode with mp3 without significant loss of quality, therefore classical music requires higher bitrates in order to encode the audio without significant quality loss.
Note again that once encoded into mp3 format, the original waveform will change. It may retain a resemblance to the original frequency spectrum and the original waveform, but it is not the same. Again, once you encode, you lose data and you're not getting that data back, unless you go back to the original PCM WAV.
Data storage is cheap these days and the only reason you would use mp3 is for a particular device support.
There are much better codecs out there now since mp3 was developed. Opus is arguably the best overall codec followed closely by AAC variants.