Metalcore is basically an evolution of the mixing of punk and metal that has been hapening for at least 30 years. In the begining bands like Minor Threat, Bad Brains took on a harsher edge to punk music and played it fast. Their speed influenced the first wave of thrash metal like Slayer, Metallica, Megadeth, etc... From there you had crossover wich was a completel blend of punk and thrash with bands like DRI, Whermacht, The Accused, Attitude Adjustment, etc. Also at this time hardcore was coming into it's own with the likes of The Cro-mags, Agnostic Front, Sick Of It All. Now you add influences of death metal from the early 90's and the fierce speed of late 80's crossover bands like Cryptic Slaughter and grind bands like Carcass and Napalm Death, especially the melodic death sounds sounds of At The Gates and In Flames and you have metalcore. More metallic and generally a more technical style of hardcore with breakdowns and clean sung parts as well for better or for worse.
Metalcore: Killswitch Engage, Unearth, Zao, Lamb Of God, Between The Buried And Me, All That Remains, Misery Signals, The Dillinger Escape Plan, Burnt By The Sun
Hardcore: Terror, Most Precious Blood, Converge, Comeback Kid, Nora