The first is the setup. This is the part that lets you add people. Basically, you can add a name, e-mail address, and birthday, to the year. In addition, you can customize by picking a specific icon for each person, and how early you want to be reminded, like 14 days before.
The other half is a little program called "Check now", that -when run- lists all upcoming birthdays. For example, it will list like "Jon will be 19 on Monday 01/23/10 (in _ days). Keep in mind, it will only show per the setting that you chose, like 14 days ahead for Fred, or 7 days ahead for Ethel.
The most practical way to use Birthday Reminder is to set it up, then add Check Now to the startup list, so every day when you startup your computer, you'll see upcoming birthdays. The program is only around 400kb in all, so it's fairly light. There is also BirthdayReminderPortable, available on the same site.
Birthday Reminder, to me, is a really useful tool for those who don't use a calendar program or online service, and just want to be reminded once a day.