(covers information from several alternate timelines)
Biomatter is organic material, such as fruits and vegetables. (ENT: "Broken Bow")
On Earth, when transporters were first approved for biomatter, there were protests. (ENT: "Daedalus")
In 2371, Kasidy Yates was transporting unstable biomatter. She was unable to beam it into her freighter's cargo bay, as she was using a Mark V transporter. Mark VI transporters were also incapable of doing so. (DS9: "Family Business")
In 2377, The Doctor conducted studies on preanimate biomatter from a comet, which consisted of a cytoplasmic matrix with an undeveloped nucleus containing primitive DNA. (VOY: "Body and Soul")
In an alternate timeline, Starfleet experimented with the drug chronexaline to protect biomatter from tachyon radiation. (VOY: "Endgame")