Anti-Matter Warp Cores are used to activate Hyperspeed or Warp Speed and allow ships to travel faster then the speed of light, but due to the destructive nature of Anti-Matter, the cores have 5 layers thick of heavy secondary sheilds around them, and an anti-matter containment structure to prevent catastrophe while on board a ship. However, if a warp core is damaged, it may cause an extremely dangerous outcome known as a "Warp Core Breach" where all anti-matter containment is lost and causing the ship to explode violently. Anti-matter was first made into use by USSR scientists and other countries adopted the idea of using anti-matter to power Hyperspeed for ships. But Anti-matter is also a high security risk due to its destructive nature..
Almost all spaceships have Warp Cores, though Russian and Geth ships have mostly turned to the much safer and stabler Mass Effect drive cores to prevent deaths, as well as managing to go even faster than before.