This word has been used ambiguously. Sometimes it means 'every two years'; sometimes it means 'twice a year', or 'every six months'. The difference is significant: in mathematical terms, a factor of 4.
The best advice we can give to avoid such ambiguity is to re-phrase words with bi- whenever you want to express 'two' and 'year' in the same phrase. Say 'twice a year', or 'every two years'
In the original Latin, there was no ambiguity. Now there is. Some efforts have been made to use biannual to mean 'half-yearly', or 'twice a year', and reserve biennial for the older meaning of 'every two years'. Many people, however, ignore this distinction; and it is too subtle to be clear, especially when talking.
In the English language, the difference appears to come from the transatlantic divide. According to C.T. Onions (The Oxford Dictionary of English Etymology, Oxford, 1966; s.v. bi-), "On the model of biennial, bi-monthly, bi-yearly ... are used for 'occurring every two months/years'; but in U.S.A. formations of this type are used for 'occurring or appearing twice in a --' (otherwise expressed by semi-)." (The same is true of their Latinate equivalents, bi-mensual, bi-hebdomodal, bi-diurnal etc.)
OED itself says, about the prefix bi-, at meaning 4:
- "Lasting or continuing for two ; occurring or appearing every two ; as BIENNIAL, bi-hourly, bi-monthly, bi-weekly.
- b. Occurring or appearing twice in a ; as in bi-diurnal, bi-monthly, bi-quarterly, bi-weekly, bi-winter, bi-yearly. (The ambiguous usage is confusing, and might be avoided by the use of semi-; e.g. semi-monthly, semi-weekly; cf. half-yearly.) [Our underlining.]"
Among other quotations in evidence in OED, two are very clear, I think: one from a biology text of 1856: "A *bi-diurnal visit from the tide." (The tide of course comes in twice a day - and 'diurnal' means 'daily'). The other is from Bible scholarship in 1885: "The *bi-weekly fast of the Pharisees... The days chosen were Thursday and Monday."
- For general information on words like biennial, see -ennium.