There are three stats, which can each be raised to 100 points. Your character can have a total of 225 stat points.
Strength - Determines your number of hitpoints, the total weight you can carry, and melee damage with weapons.
Intelligence - The amount of mana your character can have for casting spells.
Dexterity - Your character's total stamina, and the speed with which you swing/shoot weapons.
Stats are raised by using and gaining skills. You can only gain 1 stat point every 3 minutes. There are a number of skills that can be used to raise each stat.
To raise strength, use any melee skill, arms lore, animal taming, mining, lumberjacking, blacksmithing, or carpentry.
To raise intelligence, use any lore skill (ie. evaluating intelligence, anatomy, animal lore, etc.), magery, meditation, cooking, detect hidden, healing or veterinary skills.
To raise dexterity, use archery, fencing, musicianship, hiding, snooping, stealing, lockpicking, tailoring, or tinkering.
Please note: if you are at the skillcap (700 points) you can still gain stats by locking all skills except a skill that uses the stat you want to raise and then using that skill. For example, to raise strength lock all skills, then point arms lore up, and then use arms lore on a weapon repeatedly.