It shows an average of positions on the result page. (sum of positions divided by number of impressions) whole number means there was only one impression, or the average computes as integer.
See this test: http://moz.com/ugc/testing-the-accuracy-of-avg-position-for-search-queries-in-google-webmaster-tools
Beware - averages of ordinal values (i.e. ranks) are not what they actually appear to be. Serps positions are ordinals - they don't have a normal value distribution.
The sum of traffic from positions 1 + 5 does not equal the traffic of (3+3 or 2+4) - but all have an average of 3. In fact the value drops off exponentially (it also varies a lot with query type etc).
on the statistical side see: https://stats.stackexchange.com/questions/67551/calculate-mean-of-ordinal-variable