The Inception Date is the date when an elf started it's life as an embryo, which is about 9 months before the birth. Elves don't treat the day of birth as more special than other milestones in an infant's growth, and are counting their age from the day of inception. However, they don't pay a lot of attention to age in general, and this date is mostly relevant for official stuff.
According to Mr. Forkle, the reason that humans count from birth is probably because they can't accurately detect the day of the inception, and also because a large amount of pregnancies are terminated before birth. Elves can detect the exact moment of inception by the mother's belly button popping out and turning pink. Also, a loss of a pregnancy is very rare between the elves.
In Neverseen, during the official arrangements for the attendance of Sophie Foster and her friends to Exillium, Sophie discovered the difference between the way humans and elves count age. It was then revealed that she's actually nine months older than she was considered before, and even older than Biana Vacker. In the same conversation, Mr. Forkle also said that when he planted Sophie in the body of her human mother, on his identity as a fertility doctor, her belly button surprisingly popped out and turned pink - similar to elvin mothers.