What does a stat over 100 mean?

Solution 1:

The maximum hit chance you are gonna get is 100%, even if you theoretically have more that that.
But, and this is important, the total value of 105 (from your example) will be taken into calculation when an enemy is behind cover and thus lowering your hit-chance.

Example calculation:
85 Aim
+ 10 Scope
- 20 Low cover
= 75 Hit chance

Also have a picture:


Keeping these examples in mind, if you are able to boost the aim of a soldier with a bonus or 2 up to 120 you will render low cover useless to enemies.

Solution 2:

Having a 100 Aim does not mean a 100% chance to hit - enemy's defense bonuses will lower it. To have a 100% chance to hit against a sectoid in high cover (-40% to hit), you'd need an unattainable 140 aim, not to mention enemies with defense bonuses. The same principle applies to other stats - it is almost always beneficial to to have more than a 100 in a stat.