Skill level is a measure of the competence of a character in a given skill. This is based on skill ranks, but with all applicable modifiers added. The character sheet reports skill levels, but only takes into account modifiers that are applicable to all checks with a given skill. (For example, the bonuses from favored enemy only apply when a check is made against creatures of certain races, so these bonuses are not reported on the character sheet.)
For most skills, the skill level is the sum of skill ranks and an ability modifier, with the exact ability depending on the skill. Other modifiers that are added when appropriate are the armor check penalty, skill synergy, bonuses from feats, and modifiers from items and effects. (However, these other modifiers are not displayed on the character sheet during character creation.) Modifiers from items and effects stack, but there is a +50 cap on these. A skill can have a skill level even when a character has no ranks in that skill, but only if that skill allows untrained skill checks and is available to at least one of the character's classes. (Perform is the one skill that allows untrained skill checks but that is not available to all classes.)
Of the feats that improve skills, skill focus and epic skill focus are the ones capable of improving almost any skill. (The one exception is ride, which was added in patch 1.69, but no corresponding focus feats were added.) The remaining feats that improve skills only improve one or two skills, so are better mentioned in the context of those specific skills.
A size modifier is applied to stealth and detection skills, but this is considered part of those specific checks, not part of the skill level (the size modifier is neither reported on the character sheet nor used in custom scripts that do not explicitly add it).
The theoretical maximum for a skill level is 168 (in lore, for a bard), but the game is designed with an assumption that skill levels (and the DCs for skill checks) will not exceed 127. A cap enforces this assumption on skill levels in most cases, and incorrect numbers are displayed for DCs that exceed this limit. Fortunately, this is usually not an issue. A more typical maximum skill level is 70 without bonuses from items and effects (coming from 43 ranks, plus 14 from an ability, plus 13 from epic and regular skill focus), or 126 with bonuses (+50 from direct bonuses and +6 indirectly from ability bonuses). Thus the game's limit would only come into play in extreme cases when there is another factor involved, such as a racial bonus to the relevant ability or a bonus from a feat other than epic and regular skill focus.