There are various types of Necromorphs with various roles, but most of them are tasked with the purpose of creating more dead bodies for the Infector, to morph into another Necromorph. They are controlled by a Hive Mind creature which organizes the creatures. They do not need blood or air to function(They are known to operate in the open vacuum of space with little effect to them) so normal wounds that would normally kill a human, heavy blood loss, damage to the internal organs, and deep cuts will not effectively neutralize them.
The best way to effectively kill(as close to death as possible at least) a Necromorph is dismemberment. Where you must essentially cut the creature to pieces to prevent it from continuing it's attacks. This means you have to cut off it's legs, it's arms, anything to prevent it from being able to effectively move(In some cases you have to fight off reanimated limbs themselves). Whether this actually kills the creature remains up to debate, but it remains more effective than mindlessly firing rounds into the main body to no effect. The simple fact of not knowing how to effectively fight these creatures has cost many their lives, including a colony of miners Aegis 7, the USG Ishimura with other a thousand people on board and an entire ship of trained military soldiers that were armed.
The first recorded appearance of these creatured was hundreds of years ago(assuming in the future none the less) before Dead Space took place on the planet of Aegis 7, when a divine relic of alien origin known as the Black Marker that was found on Earth prior and hidden away and reversed engineered by the government to create what was known as Marker 3A, the Red Marker. A recombinant life form that was copied and recreated the DNA of the life form using what was listed on the Markers. From there it remained dormant until one of the researchers did not effectively go through the decontamination procedures allowing a few skin cells to interact with the alien life form which sprang to life re animating the dead cells. They then discovered the Marker created a field of "Dead Space" which prevented the Necromorph infection from spreading effectively neutralizing it when in the field. While continuing their research into the Marker and this new life form. Another accident in which two people failed to properly go through decontamination fully allowing the new life form to infect them. This of course led to the two of them becoming quarantined and to their eventual deaths from the infection. Then soon after to their transformation into the first two Necromorphs(that we know of at least on Aegis 7) a leaper and infector which both promptly kills and morphs everyone eventually. Before all of these scientists perish one had a vision(From the Marker) which gave him the idea to create a pedestal which would amplify the Red Marker's *dead space* field effectively containing the infection, the Hive Mind and the various other Necromorphs on this planet, until the Markers removal off its Pedestal hundreds of years later by the USG Ishimura and it's colony of miners.