A unique visitor is a host that has made at least 1 hit on 1 page of your web site during the current period shown by the report. If this host make several visits during this period, it is counted only once.
The period shown by AWStats reports is by default the current month.
However if you use AWStats as a CGI you can click on the “year” link to have a report for all the year. In a such report, period is full year, so Unique Visitors are number of hosts that have made at least 1 hit on 1 page of your web site during those year.