Enthusiasm doesn't relate, per se, to anything miraculous. Enthusiasm, in its original sense meaning "god-within" is the notion that experience of God is purely immediate (literally, as in
without mediation); the Lutheran confession is our experience of God is mediated through Word and Sacrament, through the Church; because Christ our Mediator is here with us in His Church, in Word and Sacrament.
A classic example Enthusiasm from the Reformation era would be
Thomas Müntzer/Müntzerism. Essentially, the idea that I have direct, personal access to God through my own interior experience of God entirely apart from Scripture, apart from the preaching of the word, apart from the Sacraments--through immediate revelation and experience. One does not, properly, need Scripture, or need the external operations of the Church's ministry--one need only have direct immediate experience of God. Thus personal revelation through dreams or visions were equal, or even superior, to Scripture.
Where the miraculous comes into play here is the idea that alleged miracles, or "signs and wonders" provide evidence of doctrinal or theological truths entirely apart from the received faith. That is, to say that I can reject solid biblical exposition and teaching and the received confession of faith because "such and such" miracle, or sign, or wonder "proves" the "truth" of the alternative. This is precisely why, we Lutherans, would insist on why it is so important to test the spirits. It's also why Luther went so far as to say that if something claims to be God or from God, but is apart from God's own Self-giving of Himself in Word and Sacrament, then it's not God at all, but the devil. God would never lead us away from Word and Sacrament to something else, they are His precious Means of Grace, He is there, present in these Gifts for us. So a miracle that denies the truth is no miracle at all, but can only ever be a charlatan's trick or a diabolical delusion. What my Orthodox brethren would identify with prelest.
-CrypptoLutheran