Your character has an overall "Level," but there are also several Skill trees that can be leveled up independently which altogether contribute to your overall Level. These Skills include:

Alchemy - Create magical potions and deadly poisons
Illusion - Manipulate the mind of the enemy by casting spells like Fear, Calm, and Invisibility
Conjuration - Governs raising the dead and summoning creations from Oblivion, as well as Soul Trap and bindings
Destruction - Harnesses the energies of fire, frost, and shock
Restoration - Controls life forces by casting spells like Healing, Turn Undead, and magical Wards
Alteration - Manipulates the physical world and its natural properties with spells like Waterbreathing, magical protection, and Paralysis
Enchanting - Involves binding magic to weapons and armor
Smithing - Involves crafting and improving weapons and armor from raw materials
Heavy Armor - Makes Iron, Steel, Dwarven, Orcish, Ebony, and Daedric armors more effective
Block - Reduces the damage and staggering from physical attacks
Two-Handed - The art of two-handed weapons such as greatswords, battle axes, and warhammers
One-Handed - The art of one-handed weapons such as daggers, swords, maces, and war axes
Archery - The use of bows and arrows
Light Armor - Makes Hide, Leather, Elven, and Glass armors more effective
Sneak - Moving unseen and unheard, even in plain sight
Lockpicking - Used to open lock doors and containers faster and with fewer broken lockpicks
Pickpocket - The stealthy art of picking an unsuspecting target's pockets without being caught
Speech - Used to get better prices from merchants, and persuade others to do as you ask

Assuming you have plenty of space available in your inventory, you should always pick up extra weapons, armor, items, etc. that your enemies drop even if they're not better than the ones you have. Why? When you go back to town, you can sell all of it, giving you a lot of gold in the process. You can then use this gold for whatever you actually need to purchase.