Research on Post-traumatic Stress Disorder (PTSD) has shown how the stressors associated with PTSD make changes not to the structure of a gene but to how that gene functions. In simple terms, there are chemical changes (a common one is methylation) within a gene that cause that gene to change how that segment of DNA is transcribed. Whenever DNA is replicated a copy is made. Changes within the DNA due to stress actually alter how that copy comes out. Think of it as taking a crisp, clean original document and putting it on a copy machine. Only right before you close the lid you accidentally spill a small amount of your coffee on the paper to be copied. When the copy comes out of the machine it's going to look different from the original due to the smearing of the ink from your coffee. Now when copies are made from that copy (passing your genes on to your offspring) there DNA looks different from the original (your DNA). They could then express that difference by increased anxiety, risk for PTSD, depression or a host of other psychological problems. In the research on animals that is modeled after PTSD one of the problems that are seen in offspring of animals exposed to extreme stressors is the enhanced suppression of cortisol in response to a stressor. Cortisol stops the release of adrenaline, which in turn helps the person to return to a state of less intense reactivity. So a child of a person who has experienced severe stressors may not be able to turn off their adrenaline response to stress as easily as they should. This could lead to not only emotional difficulties but an increase in stress-related illnesses. It has also been speculated that Epigenetic-mediated changes (changes from stressors experienced by the person) in the hippo-pituitary-adrenal axis (HPA axis) could create an increased vulnerability to PTSD if the person experiences trauma.
Based on the research on severe stress and PTSD many scientists are extrapolating that there could be numerous life experiences that we transmit to our children via changes in our DNA. This certainly does not mean that our children are doomed, only that there are complex ways in which we transmit our ongoing experiences to our children. It also means that our current experiences may alter the ways in which our own body creates new cells, which in turn may change how our bodies respond to stress. But if negative experiences like severe stress can cause changes to our DNA, than positive experiences such as psychotherapy and the results of psychotherapy can potentially create positive changes in our DNA as well.