From the Unofficial Elder Scrolls Pages:
Luck is an Attribute that affects everything you do in a small way, from attacking, to the chance of successfully enchanting an item.
Luck is special in that it is not the governing attribute for any particular skill. Thus, Luck never receives a bonus multiplier when you level up, and can only increase +1 per level. Most effects from good Luck can be achieved by trial and error with use of quick saves, but a high Luck is quite handy in many situations, including lock picking and alchemy. If you choose to never increase your Luck in level-ups, you might want to create a Fortify Luck spell, enchantment, or potion for those occasions when you need to be extra lucky.
Luck is very important for mages, because it increases the chance to successfully cast spells. In Morrowind spells can be created that have a chance of 0% of being successfully cast even if one has mastered the necessary skill. But with enough Luck one can increase the casting chance to any number.
Luck, however, has no effect on the quality or quantity of random loot that you find. This is an old myth that has been proven to be false.
If you have Tribunal installed, you can see the effect of Luck in combat while fighting a certain Bosmer. Gaenor's unusual high luck of 770 in addition to his level and high armor rating makes him very hard to hit.