When a material is heated the distance between individual atoms will change. For most materials the atoms get, on average, further apart (although there are some exceptions). Since the change is the same for all atoms, the total length change depends on how many atoms are in the length. This makes the length change proportional to length. You would expect this, of course; if a 1 meter piece of metal changes length by some small amount, a two meter piece would be expected to change by twice the amount.
Also, for small changes in temperature the length change is proportional to the temperature change. The constant of proportionality is called the coefficient of thermal expansion, denoted by the Greek letter alpha (a). This coefficient is not really constant over large temperature ranges, which as we will see later, can cause problems.