So while the Fireball spell could potentially be cast by a low level character, vendors will not sell the Tome necessary to learn the spell until the player's Destruction skill reaches 45-50. Items offered by vendors can actually scale according to specific Skills or Perks. Since levels of NPC followers are determined by the level of the player during their first encounter, certain followers such as Lydia can become obsolete fairly early on in the game (PC players can fix this via the console). Level scaling also affects the game in more subtle ways. Certain areas have minimum or maximum levels, so it is possible for the player to encounter enemies who are significantly more or less powerful. For example, the player will randomly encounter Dragons early on, with stronger Blood Dragons showing up starting at level 15 to 20. It is still present, though, and in most areas the level (and sometimes types) of enemies present is based on the player's level. Skyrim's level scaling is MUCH less pervasive than Oblivion's - no more bandits in full Daedric Armor. This effectively removes the overall level cap (originally 81). This will reset the skill to 15, return its perks and allow the skill to affect leveling again.
For every level gained, the player will also be given a Perk point, which can be invested in the various perks in the skill trees.