I can see three primary meanings of the word:
"the universal laws of Nature are merely God's decrees... So if anything were to happen in Nature contrary to her universal laws, it would also be necessarily contrary to the decree, intellect, and nature of God. Or if anyone were to maintain that God performs some act contrary to the laws of Nture, he would at the same time have to maintain that God acts contrary to his own nature."The key to understanding this argument is in the definition of "Nature". Implicit in the argument is the idea that "Nature" is all that there is - even God is subject to its laws. This is called "monism", and today the Unitarian religion explicitly equates God with all of Nature. Making Nature universal, makes "natural causes" equivalent to logical necessity - making "miracles" a contradiction in terms. In other words, by starting with the presupposition that there is no supernatural, any talk about the supernatural is illogical.
Schleiermacher takes the Deist aproach and states that God ordained a "system of Nature" as a "closed causal nexus" - i.e. a system with no supernatural intervention, hence supernatural intervention is illogical.
Others, like Hume (and Aurthur C. Clarke), were more skeptical, and simply observed that we can never be absolutely certain that a given event is a miracle, since there might be some Natural cause (or advanced technology) of which we are not aware.
The logical claims of Schleiermacher and Spinoza are a matter of blind faith. If you start with the assumption that there are no miracles, then you can only reach the conclusion that there are no miracles. In light of our own creations, their assumption seems silly.
The epistemological claims of Hume boil down to the question of whether it is possible to rationally determine whether a given event is due to natural, or to intelligent causes. While Hume is right that absolute certainty by reason alone is impossible. The point of this course is that measuring the "designedness" of an event is an exercise in science that we undertake in many different fields as a matter of course.