Its not an exact increase like 5% luck = 10.5 explore rate

From what i gather its this:

When you explore and it says 10 acres per turn you might get 8,9,10,11,12 etc etc

So in their forumulas for missiles and explore they have a random fact. It increase the random factor positively by 5%.

So gives u a higher chance of getting 11 acres or 12 acres per turn.