Skill ranks are a measure of the training a character has in a given skill. These are acquired solely by spending skill points during level-up (and are generally only seen during level-up; the character sheet reports total skill level). Ranks are the base to which other modifiers, such as an ability modifier, are added. Ranks are the criteria used when a class or feat has a skill prerequisite.
Many skills can be used even if the character has no ranks in them; doing this is called making an untrained skill check.