When you level up Mining for example, the game will state that you get +1 in Mining proficiency. What does this actually do?
Does it decrease the amount of swings needed to smash rocks?
Or does this just mean that you leveled up 1 level?
Though it displays as a whole number, under the covers your character's stamina can have decimal values. Levels in applicable skills reduce, by a fractional amount, how much stamina it takes to use the tool. Here are the ones I was able to figure out.
These skills cause you to use 0.1 less stamina per skill level with these tools:
Foraging
Fishing
Farming
Mining
These always use 4 stamina:
(Source: I used a decompilation tool to peek at the source code.)
I'm not sure about anything else, but higher Proficiency decreases the amount of energy usage for tools. I haven't upgrade my base Hoe at all but, without any hard numbers, I can say that I can till more spaces for the same amount of energy than when I started out.