The Hybrid was a creature created by the Asurans as a weapon against the Wraith. Rodney McKay explained that it was Oberoth's pet project and was probably made as part of an arms race they likely started when the Atlantis expedition reactivated the Wraith attack code.
The hybrid's initial purpose was to make more Replicators out of its enemies. Using its ability to hide itself, it would sneak around a planet or hive ship or wherever it was dropped and turn the people there into new hybrids. The creature had to be a hybrid, as living tissue was infectious, so technically the hybrid was part Replicator and part disease. Unfortunately, when it was created the Replicators underestimated the power it needed to function as it required massive amounts just to live. The hybrid went insane with power lust as a result. At that point even the Replicators couldn't control it and they tried to destroy it, but failed. A problematic part of the hybrid is that parts blasted off or detached can still live separately from the main body of the hybrid.
In 2007, the hybrid decided to infiltrate Atlantis for the people and power there. It created a construct named Angelus using Elizabeth Weir's memories, which were in the Asuran database that it had access to, to make a story for Angelus that the Atlantis expedition would believe. The hybrid disguised itself as Angelus' ship and the two ended up meeting up with the Apollo. The hybrid left part of itself behind there and once it got to Atlantis began to act. It absorbed Angelus, having no more use for him, then tried to absorb power from the Zero Point Module. Colonel Sheppard attempted to destroy it with drones, but failed, so he rammed the hybrid with a Puddle Jumper while it was climbing the main tower. All this did was merely stun the hybrid, but it allowed Angelus, whose mind remained intact despite the absorption, to gain some control over its basic functions and save Sheppard. Angelus, using Sheppard's blood and Ancient Technology Activation gene, created a poison out of those ingredients with the hybrid's ability to manufacture whatever it needed- exploiting the fact that the Hybrid's artificial immune system couldn't defend against something that it didn't know was there) and spreads it to the hybrid while its still knocked out. Angelus then helps Sheppard escape, just before the hybrid wakes up. The poison works and the hybrid slowly dies over several days and dissolves into M35-117's ocean.
On the Apollo, after a lot of work, the crew managed to succeed in damaging the piece of hybrid on board and blew it out the bomb bay doors into the atmosphere of a gas giant. Once the hybrid descended far enough into the atmosphere, the atmosphere crushed it, killing that part of the hybrid. Afterwards, the Apollo was searched for smaller pieces and a lot were found, most dead, but one still alive. That tiny piece was killed with an arc welder and it and the rest were blown out of an airlock. The Apollo then traveled to the facility where the hybrid was created and destroyed it with the help of an Asuran cruiser to ensure that another hybrid would never again be created. (SGA: "Angelus")