This is a perennial (ha, ha – see what I did there?!) mix-up and it’s worth just setting these words down for everyone – but I would maybe even advise that you don’t use them yourself, limiting yourself to using the explanation rather than the word. Then no one will be confused, and no one will turn up for a biennial party that they think is biannual!
Biennial means occurring every other year. So a biennial event might happen in 2010, 2012 and 2014. It won’t happen more than once in a year, and it won’t happen in the years in between.
Biannual means occuring twice a year. Usually regularly – so you might have a biannual event taking place in February and August every year, for example, six months apart. So a biannual event will happen twice a year, every year, so in our above example, twice in 2010, twice in 2011 … twice in 2014, etc.
There are more of these words floating around too – for example, bimonthly. The dictionaries and other reference materials do actually suggest avoiding these, in order to avoid mistakes, and to use “every two months” instead, and as I mentioned above, I think this is a good precept by which to go. So that biennial event can become an event that happens every two years – then we all know where we stand.