Cost-push inflation occurs when overall prices increase due to increases in the cost of production. Higher costs of production can decrease the aggregate supply (total production) in the economy. If the demand remains unchanged, the prices of commodities increase causing a rise in the overall price level which then is passed on to consumers creating cost-push inflation.
On the other hand, Demand-pull inflation exists when aggregate demand for a good or service outstrips aggregate supply. It is the most common cause of inflation.
Apart from the rise in prices of inputs, there could be other factors leading to supply-side inflation such as natural disasters or depletion of natural resources, monopoly, government regulation or taxation, change in exchange rates, etc. This is inflation triggered due to supply-side constraints.