Women who are over 35-years-old at the time of delivery are considered to be of advanced maternal age or AMA. This category was created primarily because of the increasing risk of Down syndrome, which is 1 in 270 at age 35. This cut-off was picked many years ago because it was the expected pregnancy loss rate when genetic amniocentesis was performed; at the time invasive testing like amnio was the only choice, and it made sense to only offer it to the highest risk women.
Today, we have many better tests available to screen for Down syndrome and we know that the rate of pregnancy loss with genetic amniocentesis is dramatically lower than 1 in 270.
Apart from this increased risk of Down syndrome, being over 35 may not mean much of anything. Typically, as women get older, they may gain extra pounds and extra illnesses that would tend to complicate pregnancies. Yet, a healthy woman of normal body weight above age 35 who does not have a pregnancy complicated by Down syndrome should expect to have a better and safer pregnancy than a woman 10 years her junior who is obese or has a preexisting medical condition. So your doctor should individualize what your age means for you in the context of your total health status.
Women today frequently delay childbearing until after age 35 and while this does increase their risk of miscarriage and conditions like Down syndrome, most have pregnancies whose outcomes are similar to those of younger women.