Step 1: Recall the meaning of the word.
Biannual is built from the prefix bi, meaning two, joined with annual, meaning yearly. So biannual describes something that happens two times within a single year.
Step 2: Check each option.
Option A, once in two years, actually describes the word biennial, a different term that is often confused with biannual. Option B, every year, describes annual, which happens only once a year, not twice. Option D, after every two years, again matches biennial, not biannual.
Step 3: Pick the matching option.
Option C, twice a year, is the correct sense of biannual, since the event occurs two times in one year.
Final Answer:
Biannual means occurring twice a year, so option C is correct. \[ \boxed{\text{C}} \]