The breeding tank (named only in mission orders from Adam) is a room in Sector 4 in Metroid Fusion. It is a room in which Serris, a specimen Samus was sent to terminate, often returned to before being infected with the X Parasite.
Thinking the Serris would be encountered here, Adam even pinpointed a boss icon in this room in the map data given to Samus, but upon entering the breeding tank, she came upon the original Serris's remains (consisting of bones only). Samus moved on to the next room, and found an X mimicking a Gadora, indicating the presence of a powerful X creature. The following room is where Samus battled and defeated the Serris-X.
Interesting to note is that the breeding tank seemed relatively small for the large Serris, giving the impression the creature had restricted movement in it. It's unclear why the Serris was placed in a breeding tank, as no other specimens of the species are ever encountered- this may indicate that the Serris was capable of asexual reproduction.