The oil crises of the 1970s contributed to recessions by lowering aggregate supply, resulting in the crippling stagflation of that decade.
Oil is a hugely important commodity because it is part of the price of essentially everything in our economy. Oil goes into the price of things we buy because it is used to transport them and perhaps to make them. This was even more true in the 1970s before steps were taken to reduce America's consumption of oil (as compared to its GDP). So, when the oil crises happened, the price of producing goods and services increased. This leads to a left-ward shift of the aggregate supply curve. When aggregate supply shifts to the left inflation occurs and output declines.
In short, then, oil shocks made it more expensive to produce goods and services. This tends to lead to a recession until producers can adapt and find cheaper ways to make their products.