Assuming you’re speaking about a song that is labeled as “Live acoustic”
“Acoustic” is a way of saying that the instruments in the song are not electric. A guitar is going to be wood, bass will be stand up, there will be no mixing board work etc.
“Live” is indicating the song was performed in a show in a single take, rather than in a recording booth with multiple takes.
With regards to music recordings:
Live means it is a song played as if in front of a live crowd – the musicians are all playing together, and get one take to play the song. This is in comparison to a studio recording where a song can be recorded in countless different pieces which are then ‘assembled’ into the final recording – every instrument may be recorded separately, they can make multiple recordings for each part and choose the best ones, and they can do things like layering tracks to do things that are impossible in real life such as having a vocalist or instrument paying multiple different parts at the same time.
Acoustic refers to using acoustic instruments. Most bands use electronic instrumentation, which means they can include amplifiers, effects units and other audio processing to alter the sound they produce – the distorted guitars heard on most rock music for example are a result of specific effects and amplifiers.
To play acoustically is to use more traditional acoustic instrumentation without these additional tools and often results in simpler, more natural sounding versions of songs.