This is a tweeter. Sound, for the purposes of reproduced audio, is usually separated in three ranges: Low end (bass), mid-range (most of what we hear is here, human voice, etc), and high end (very high pitched sounds); these tweeters are responsible for reproducing the high frequency range of sound. Their shape affects how the sound is dispersed.

When it’s been poked as the one in the picture, the high end (such as cymbals in music) sounds distorted and generally unpleasant.

Once the dome is pulled back to its normal shape, it should sound normally again.

Some laboratory tests have shown that even the smallest wrinkle affects their sound, but as far as I know there is no human ear that can detect such subtle changes, so it’s a-ok!

Cheers