Step 1: Source of silk
It comes from the cocoon of the silkworm, which is an animal.
Step 2: Eliminate
Vegetable fibres come from plants, synthetic fibres are made from chemicals, and semisynthetic fibres are modified cellulose.
Step 3: Conclusion
So silk is an animal fibre.
Final Answer:
Silk comes from an animal source, so it is an animal fibre.
\[ \boxed{\text{(C) }\text{Animal}} \]