The kinetic product is the product that requires less activation energy to start the reaction but is less stable, so in lower temperature reactions (a 'low temperature' is relative based on the reaction) the kinetic product will form. This is because there is less energy available in low temps, and the thermodynamically more stable product requires a higher activation energy than the kinetic product. If the temperature is raised enough, there will be enough energy that the activation energy required for the more stable product's reaction will be met more easily, so the thermodynamic product will be formed. Also, over time some of the kinetic product will eventually become the thermodynamic product even at lower temps.
The best example I can think of is 1,2 (kinetic) versus 1,4 (thermodynamic) addition reactions in a diene.