Unique Visitor:
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.
You can click on the "year" link to have a report for all the year. In such a 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.

Visits:
Number of visits made by all visitors.
Think "session" here, say a unique IP accesses a page, and then requests three others without an hour between any of the requests, all of the "pages" are included in the visit, therefore you should expect multiple pages per visit and multiple visits per unique visitor (assuming that some of the unique IPs are logged with more than an hour between requests)

Pages:
The number of "pages" logged. Usually pages are reserved for HTML files or CGI files, not images nor other files requested as a result of loading a "Page" (like js,css... files).

Hits:
Any files requested from the server (including files that are "Pages")

Bandwidth:
Total number of bytes downloaded.

Entry Page:
First page viewed by a visitor during its visit.
Note: When a visit started at end of month to end at beginning of next month, you might have an Entry page for the month report and no Exit pages.
That's why Entry pages can be different than Exit pages.

Exit Page:
Last page viewed by a visitor during its visit.
Note: When a visit started at end of month to end at beginning of next month, you might have an Entry page for the month report and no Exit pages.
That's why Entry pages can be different than Exit pages.

Session Duration:
The time a visitor spent on your site for each visit.
Some Visits durations are 'unknown' because they can't always be calculated. This is the major reason for this:
- Visit was not finished when 'update' occured.
- Visit started the last hour (after 23:00) of the last day of a month (A technical reason prevents AWStats from calculating duration of such sessions).

Grabber:
A browser that is used primarily for copying locally an entire site. These include for example "teleport", "webcapture", "webcopier"...