From Omega 3 and Omega 6 your brain makes something called DHA (docosahexaenoic acid) and AA (arachidonic acid) that are then incorporated into the cell membranes. These longer chained, more complex fatty acids are also available preformed directly from food. E.g. Cod liver oil, Neptune krill oil.
A point to note here is that the brain's ability to assemble these fatty acids can be severely compromised by stress, infections, alcohol, excess sugar, and vitamin or mineral deficiencies – factors common today.
Effects of DHA loss
The DHA that your brain makes is the most abundant fat in the brain. Loss in DHA concentrations in the brain cell membranes correlates to a direct decline in functional integrity. Thus declining DHA concentrations cause cognitive impairment.
DHA and depression
Various studies have been done on the absence of DHA in those with depression. In Europe for example, populations showed rates of depression 10 times greater than in Taiwan – where people consume a lot of fish. The Japanese, whose diet is mainly fish, have a massively lower depression rate than Europe too.
Fatty acids and Alzheimer's Syndrome
Disorders such as Parkinson's and Alzheimer's exhibit cell membrane loss of fatty acids. Thus is makes sense that an optimal diet with a balance of Omega 3 and Omega 6 fatty acids may help to delay their onset or reduce the damage these diseases elicit.
Imbalance of fatty acids and mental disorders
An imbalance of Omega 3 and Omega 6 can lead to a variety of mental disorders, including hyperactivity, depression, brain allergies, and schizophrenia. A balanced ration of the two fatty acid families (Omega 3 and Omega 6) is necessary for a healthy brain. It structurally is composed of a 1:1 ratio of Omega 6 to Omega 3. However our Western diets tend to have at least twenty times more Omega 6 than Omega 3. That's an unhealthy ratio of 20:1.
This imbalance can easily be corrected by eating more Omega 3 rich fish and linseed oil, by eating less sugar, and by completely avoiding trans fats altogether. Trans fats are found in partially-hydrogenated oils, margarines you thought were healthy 'cos it says so on the label' and shortening. Cheap supermarket own branded oils and salad dressings are best avoided unless they are clearly labelled "Cold Pressed".