I am at the blacksmith in the Undead Parish and I have already upgraded my armor and weapon a few times but I have no idea what it is actually upgrading (Strength,Dexterity, etc.).
Depending on the upgrade path, it can do various things like:
- Increase or decrease stat scaling
- Increase or decrease base weapon damage
- Add new types of damage that scale on different stats.
The way you describe your situation, you are likely upgrading things along the 'normal' upgrade path. This path increases base weapon damage and increases the weapon stat scaling.
I encourage you to check out this wiki page for more information: http://darksouls.wikidot.com/upgrade
This is a good question. I know it asks for an "exact" breakdown but those can be very technical.
Upgrading a weapon may not increase its damage at all - it may increase or increase any of its damage, magical, lightning or fire damage bonuses, and its stat scaling.
Normal Weapons (Up to +15), Raw Weapons: These weapons have no elemental affinity so their effectiveness is decided most their damage type. These are some of the most important weapons because they can be enchanted with magic.
Fire Weapons (Up to Level 10): Adds fire damage, but reduces scaling bonuses. Fire weapons tend to be very effective on most enemies. Can't be enchanted.
Chaos Weapons (Up to Level 5): Adds Fire Damage but this time based on how many Humanity you're holding. Good for a character who tends to hold a lot of Humanity (Brotherhood of Sunlight, Darkwraith Covenant)
Divine Weapons: Don't do very much damage overall, reduced scaling except for faith. However, using a Diving Weapon to finish off a skeleton in the Catacombs will prevent it from being revived. Astora's Straight Sword will also do this.
Occult Weapons: Does extra damage against some enemies. Typically not very good. Can do lots of damage with very high faith (confirm?)
Magic/Enchanted Weapons: Adds stat scaling based on intelligence. Very useful if your character has high intelligence, otherwise doesn't do much damage.
Lightning Weapons: Tend to be quite strong. Like fire weapons, tend to knock enemies back. Low stat scaling. Best for builds that don't rely too much on scaling.
Boss / Dragon Weapons: These weapons may have properties similar to magic, lightning or fire weapons.