Yoga is absolutely safe for your baby. While yoga in general can range from a gentle relaxation to a rigorous heart-pumping work out, prenatal yoga is specifically designed to feel good for mother and not harm growing baby. As your pregnancy progresses you may find that some poses you could do easily in the first trimester, are now quite difficult with your beautiful, round belly in the way. Not to worry! Poses can be easily adjusted to each individual body at each stage in the pregnancy.
Prenatal yoga poses are specifically designed to help women adapt to the physical changes of pregnancy. For example, some yoga poses will help strengthen the legs (now responsible for holding more weight), while others will focus on opening the hips (important for growing baby and birth), or alleviating back pain (from the extra weight of the front body). Breathing exercises done in prenatal yoga will also help women to relax during pregnancy and prepare for birth. Additional poses important to prenatal yoga are restorative (or relaxing) poses that support the woman in a reclined, or semi-reclined, position where she can relax without any strain whatsoever.
In general, pregnant women will want to avoid deep twisting (due to pressure on the abdominal area) and will always focus on providing ample space for their belly within a pose. That may mean separating the feet or legs wider than usual in a forward bending pose, or placing a cushion strategically to give extra space to the belly. Most backbends are also contraindicated, because they stretch the abdominal muscles.
Other poses that are avoided in prenatal yoga are most inverted poses where the uterus is above the heart (e.g. headstand) as you want to avoid anything that may disrupt blood circulation to your uterus. There are some milder inversions that are perfectly safe for you and your baby (e.g. legs up the wall pose) that will still allow you some of the benefits of an inversion.
All of these adjustments will be explained further in pose instructions though they may already be very instinctive to you. Ultimately the goal of prenatal yoga is that you are listening and interacting with your body and growing baby, and will know when (and maybe even how) to become more comfortable and supported.
