At this time there are many studies and clinical examples of 'exercise' improving brain function overall. Even more specifically, being used in treating mental health challenges. Of course we know only prescribed movement for each person will help an individual's health.

Especially these days, many have a sedentary lifestyle. A sedentary lifestyle as defined by webmd: "Sedentary means a lifestyle that includes light physical activity associated with typical activities of daily living (cleaning, eating, stairs inside, sitting, etc). Moderately active consists of walking 1.5 to 3 miles daily at a pace of 3 to 4 miles per hour (or the equivalent). An active person walks more than 3 miles daily at the same pace, or equivalent exercise."

Within the brain we have an area called the cortex, which thins as we age. This thinning can occur faster and in greater amounts depending on lifestyle!

Research has shown that you can help to prevent this thinning by limiting sedentary behaviour. That also regular moderate to vigorous physical activity can improve the cortex. But what is less clear is whether exercise can protect against cortical thinning independent of being otherwise sedentary.  To quote: "a group of scientists from British Columbia enrolled 30 adults with an average age of 61 who were enrolled in another study on increasing exercise and reducing sedentary time among adults with osteoarthritis of the knee. Activity levels, sedentary behaviour, and cortical thickness were measured from each participant.  Participant exercise and sedentary time were tracked by using fitness trackers for 7 days, and MRI imaging was used to measure their cortical thickness. An average of 70 minutes of daily moderate to vigorous physical activity was reached by the group while spending close to 12 hours a day doing nothing more strenuous than reading or using a computer outside of their daily exercise.  According to the researchers after analyzing the data and comparing brain scan high levels of physical exercise were found to be associated with greater cortical thickness, especially in the frontal areas regardless of sedentary time, and there was no link between less thickness/thinning with greater amounts of sedentary behaviour outside of exercise." (Med & Sci Sp & Ex, Falck, Ryan, Oct 2020)

This is not to say sedentary is good, but shows how powerful exercise is for the brain!

“One potential explanation is that higher amounts of MVPA [moderate to vigorous physical activity] provide a strong neuroprotective response, which ameliorates the negative consequences of too much SB [sedentary behaviour],” the study authors wrote in Medicine & Science in Sports & Exercise.
Maintaining a thick cortex with regular exercise can help to fend off dementia and brain disease, and according to this study meeting the current guidelines of at least 150 minutes per week with moderate to vigorous exercise can help to reduce the risk of developing Alzheimer’s disease by up to 38%. 

Additionally, vigorous exercise improves neurotransmitters such as BDNF, which helps the hippocampus (in limbic system of brain) and generally improves focus and short term memory.

This is just a slice of information for us to see the need for regular movement to improve our noggin (brain). Hopefully is leads to getting help with prescribed movement  to make it happen for you!