Memories are made through a synaptic-strengthening process called long-term potentiation (LTP). Prolonged stress weakens the synapses, which decreases LTP, thus having a negative effect on memory. A mouse study found that when exercise co-occurs with stress, LTP levels are not decreased, but remain normal. The exercising but stressed mice also performed as well on the memory tests as the non-stressed mice, and better than both groups of sedentary mice.
Running is mentioned specifically because the exercise the mice took involved running wheels.
Reference:
Miller, R. M., Marriott, D., Trotter, J., Hammond, T., Lyman, D., Call, T., Walker, B., Christensen, N., Haynie, D., Badura, Z., Homan, M., & Edwards, J. G. (2018). Running exercise mitigates the negative consequences of chronic stress on dorsal hippocampal long-term potentiation in male mice. Neurobiology of Learning and Memory, 149, 28–38. https://doi.org/10.1016/j.nlm.2018.01.008
