Deathcore is an metal sub genre genre and an aesthetic. Deathcore songs are very heavy, utilize breakdowns, blast beats, growled and shrieked vocals, and have very violent and shocking lyrics.
As far as the aesthetic, deathcore bands (and fans) often have a dark style, a strange combination of scene/emo, punk and metalhead. Firstly, gauged ears are very common. Sprawling, intricate tattoos (often covering the neck and upper body) complement the ears. Hair is pretty versatile, with that said a lot of deathcore fans have sweeping, emo/scene inspired spiky hair. Most important of all, the deathcore aesthetic would be nothing without the illegible band logos. A fan will be seen wearing the logos of their favorite band on everything from; t-shirts, hoodies, hats and more.