Actions of God not explained by normal laws of physics, chemistry, biology, or the natural sciences
There are at least 4 ways to define "miracle" from the most restrictive to the most inclusive described below. This tag definition adopts the second definition below.
The secular and modern understanding is too restrictive by Christian standard, influenced by Hume's unbiblical and untheological definition of miracle as "violation of the laws of nature". Read this article for more details.
The Biblical definition highlights God as the ultimate cause who may work in ways "compatible with the laws of nature", so we can define "miracle" as an event whose cause is metaphysically "above" or "outside" nature. By this definition, a miracle always has a physical component that is measurable. Thomas Aquinas identifies 3 degrees on how this cause manifests vis a vis laws of nature, in Summa Contra Gentiles Chapter 101: (emphasis mine)
-  ... The highest rank among miracles is held by those events in which something is done by God which nature never could do. For example, that two bodies should be coincident; that the sun reverse its course, or stand still; that the sea open up and offer a way through which people may pass. And even among these an order may be observed. For the greater the things that God does are, and the more they are removed from the capacity of nature, the greater the miracle is. Thus, it is more miraculous for the sun to reverse its course than for the sea to be divided.
-  ... the second degree among miracles is held by those events in which God does something which nature can do, but not in this order. It is a work of nature for an animal to live, to see, and to walk; but for it to live after death, to see after becoming blind, to walk after paralysis of the limbs, this nature cannot do—but God at times does such works miraculously. Even among this degree of miracles a gradation is evident, according as what is done is more removed from the capacity of nature.
-  Now, the third degree of miracles occurs when God does what is usually done by the working of nature, but without the operation of the principles of nature. For example, a person may be cured by divine power from a fever which could be cured naturally, and it may rain independently of the working of the principles of nature.
A more flexible definition is: Anything God does that manifests in human consciousness unexpectedly (due to its propitious circumstances), whether it has a physical component or not. By this definition, it then includes all listed below, which "by doctrine" calls for the Holy Spirit as the ultimate agent:
- unexpected conversion
- sudden "pangs" of conscience in who is normally a person of a wicked character
- strong conviction for one to become a missionary / priest / religious
- conviction of God's answering one's prayer: man overboard saved by a boat in the midst of a storm, etc.
- sudden call from God to St. Augustine saying through the voice of children playing "tolle lege, tolle lege"
- all vision, dream, prophecy, and word of knowledge
- sudden experience of joy, peace, blessedness, feeling loved by God
- sudden release from personal addiction
- freedom from possession by exorcism
- healing from cancer after a prayer
This definition is harder to verify since for some events there may not be a physical component, only the consciousness of the person experiencing it as the sole witness. Also, some may originate not from God, so require some discernment to call it "from God" (miracle), "from demon" (deception), "from self" (psychological), or "from nature" (false identification). This will become important for discerning false prophecy from true prophecy.
The most inclusive defines "miracle" as #3 above but also includes anything God does (known by doctrine) that is "expected" / "ordinary":
- Ensoulment for every conception
- Gradual conversion that doesn't include extraordinary events
- Illumination from reading scripture
- Aesthetic appreciation from general revelation through nature
Because some events occur "regularly", including these in "miracle" waters the term down, making it a term of banality. We also need the discernment and verification mentioned in #3.
Note that magic is not a miracle since the initiator agent is NOT God, but men/women (witches, shamans, satanic priests, etc.) allying themselves with demons to counteract laws of nature.