Heat capacity is similar to specific heat; it is related to the amount of temperature change due to a unit amount of energy added to a substance.

High specific heat materials, such as water, do not change their temperatures much when heat is added or taken away. So, the application to the atmospheric environment is that coastal or maritime regions do not experience a large daily temperature range because the solar radiation during the day is absorbed by the ocean/lake without a large temperature change; at night, the water emits infrared radiation to space but the temperature decreases only a little.

In contrast, for inland areas, where it's mainly soil or sand, there's a wide daily range of temperature because the temperature of the land goes up a lot more than the ocean for the same amount of insolation, and at night the temperature goes down a lot as the land loses infrared radiation to space.