The exact nature of vehinholes is unclear, though it is believed that they were mutated flora.
Their vein spread in a manner similar to Tiberium, originating from a large central mass with several animal aspects, including what appears to be a "mouth". There have been many reports of living creatures being torn apart by the veins, and it was rumored that these carcasses would then be moved to the central mouth and consumed. Dr. Gabriella Boudreau speculated that veinholes were similar to the Venus flytrap, and consume living tissue in order to spread their mass. 
Veinholes were highly agitated by vibrations and kinetic energy, and would attempt to tear apart the source of such disturbances using pseudopods formed from the vein materials. Smaller units, such as infantry and light vehicles, can usually cross a vein field before succificently agitating the veins. Once the central mass is destroyed, the remaining veins would wither and slowly die. However, the veinhole possesses a defense mechanism - when attacked, it emits clouds of highly concentrated Tiberium gas, which can corrode nearby vehicles and kill infantry.
The veins were apparently composed of solidified Tiberium gas. The Brotherhood of Nod was able to harvest them using weed eaters and weaponize them the form of Chemical missiles, which release the same corrosive gas as the veinholes when detonated.
Living veinholes were not seen following the Firestorm Conflict. Whether it was due to GDI's Tiberium abatement effort or due to Tiberium's mutation into a different form is unclear. What appeared to be dead veins can be seen on the ground of many newly-classified Red Zones, however.
Tiberium veins will continuously attack any vehicles that drive over them, but will not harm infantry (excepting jump jet infantry, due to their heavy equipment). Vehicles that are not affected by the veins include the Wolverine, Attack Buggy, Hover MLRS, Harvester, and Weed eater. The veins expand constantly, and will also destroy structures which they come into contact with, though the expansion can be blocked with concrete walls.
Killing the veinhole monster will stop the growth of the veins and cause them to recede over time, and this is most easily accomplished with a small group of Wolverines or Attack Buggies. Attacking the veinhole will cause it to release corrosive Tiberium gas clouds, although these can be easily avoided. When playing in campaign missions or skirmish mode, the veinhole can often be used to your advantage as computer-controlled units will often disregard the danger posed by the veins and drive right over them, allowing you to lure them to their destruction.
- Tiberian Sun patch 1.13: destroying a vehinhole monster will no longer crash the game after an extended period of gameplay since its destruction.