Tiberium is a highly useful source of material in the production of buildings and weaponary.
Just like Crystal, each base has a set amout of the resource sprouting from the ground and requires a Harvester placed on it to gather and proces the shards into useable material. It's main use is in the upgrading of structures in your Base and Defenses.
In battle with foreign enemies you can obtain Tiberium in bulk by destroying buildings that contain the material and in large Crates from certain specific buildings. Likewise during a PvP attack you can loot the resource by destroying the other players Tiberium rich buildings.
For the Continuous Production Bonus a Silo should be placed near by.