Heating an object gives its particles more energy, so its internal energy increases. Usually the particles move faster and the temperature rises. They also move slightly further apart, so the object expands. Gases expand the most, liquids less, and solids the least.
The specific heat capacity of a material tells you how much energy 1 kg needs for a 1 °C rise in temperature.
During melting or boiling the temperature does not change, even though energy is still being supplied. This energy, called latent heat, is used to overcome the forces between the particles and not to make them move faster. Evaporation is different from boiling: it happens only at the surface and at any temperature.