The meaning and power of Gideon's Sword is explained here:

As soon as he meets the angel of the Lord under the terebinth of Ophra, Gideon commits himself. The three chapters devoted to Gideon present us with a man of exemplary faith. Can we ask for signs from Gd? And if so, do we have to be as specific as Gideon when he claimed the signs of the fleece?

Once convinced of the identity of the messenger, he obeys God at the risk of his life.

Without a murmur, he agrees to reduce his army to 10,000, then to 300 when Gd asks him to. Finally moved by an unlimited faith, he engages in hostilities with this handful of fighters against an innumerable force. Gideon is a hero of faith. When Gideon asks for the signs of the fleece, he is not alone.
This one asks for the signs of the fleece, not for himself, but for the people. The judge knows that God will grant victory; they doubt it.

Here is the crucial point to grasp: Gideon asks God to confirm to the people the call he received in private.

“Gideon said to God: If you will save Israel by my hand, as you have said, behold, I will put a fleece of wool on the threshing floor; if the dew comes on the fleece alone and all the ground remains dry, I will recognize that you will save Israel by my hand, as you have said. It was so. The next day he got up early in the morning, pressed the fleece, squeezed out the dew, the dew from the fleece, filled a cup with water. Gideon said to God: Do not let your anger be kindled against me, and I will only speak this time: I would only like to make one more test with the fleece: that the fleece alone remains dry and that the dew comes on all the ground. And God did so that night. The fleece alone remained dry and the dew came all over the ground.” (Judges 6:36-40). He will therefore use a fleece (a sheepskin) as an intermediary between the people and God.

Several commentators have given different meanings to the miracles of the fleece.
Most agree that the dew symbolizes the blessing that comes from God and allows life on earth.
The fleece surely represents Israel, a people of shepherds, a land where life is sweet (milk and honey), like a sheep's skin is sweet.
The area around represents the nations, perhaps Amalek and the Midianites.

The meaning of the first sign: the dew on the fleece and not on the threshing floor announces that the divine blessing will rest on Israel and not on the Midianites. This can also mean that the Jewish people were chosen by God at first (the Old Testament).
The second sign is there to confirm the first and not to contradict it: the dew spreads on the floor and not on the fleece. Gideon therefore does not wish by asking for this sign that the blessing be on his enemies, but that the sign confirms the victory of Israel over Midian.

The first sign was "natural" because it is logical that the dew clings more to a fleece than to an air.
To demonstrate to the people that God is more powerful and that he will give them victory over the spiritual enemy represented by Baal, God of fertility, Gideon asks for a second "anti-natural" sign, the dew will cling to the air and not to the fleece.
Thus the people will have victory over the human enemy, but also over the infiltrated idols.