Please don’t just paste the definition from the dictionary. I’ve looked through several dictionaries and I still don’t understand this word fully. All I am getting is ” act of manifesting” “something that manifests” etc… I don’t know what “manifest” is?
I know you said that you already looked at dictionary listings, but really, that’s the way to go. If you don’t know what a word means that is given in a definition, keep looking the words up–which is what I easily did and put the answer to your question below (you just needed to go an extra step) 
Manifestation:
1. an act of manifesting.
2. the state of being manifested.
3. outward or perceptible indication; materialization. Ex: At first there was no manifestation of the disease.
4. a public demonstration, as for political effect.
5. Spiritualism. a materialization.
Manifest:
1. To show or demonstrate plainly; reveal. Ex: “Mercedes . . . manifested the chaotic abandonment of hysteria” (Jack London).
2. To be evidence of; prove.
3. 1. To record in a ship’s manifest.
2. To display or present a manifest of (cargo).
MANIFESTATION A NANTES / REDEYEF
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November 13th, 2008 at 6:25 am
The Portuguese Republic Constitution helps you define it.
In its article 45, it gives you an idea of manifestation combined with meeting.
Quoting:
“1 – All citizens have the right to gather and meet, peacefully and without weapons, even in open and public spaces, without need of approval.
2- All citizens have the right to manifestate.”
This grants all citizens the right to gather and meet to prove a point, for instance, to complain about high taxes or unfair government policies, and they meet in front of Government’s house with banners complaining and proving their point, to make known that they’re unsatisfied about something.
References :
November 13th, 2008 at 6:30 am
in simple words it can be, making " appearance " thru any medium or without medium
Edit: As Prophet Moses (may peace be upon him) saw God and had conversation with God, God manifested into glaring light / fire thru / in a tree
References :
November 13th, 2008 at 6:33 am
I know you said that you already looked at dictionary listings, but really, that’s the way to go. If you don’t know what a word means that is given in a definition, keep looking the words up–which is what I easily did and put the answer to your question below (you just needed to go an extra step)
Manifestation:
1. an act of manifesting.
2. the state of being manifested.
3. outward or perceptible indication; materialization. Ex: At first there was no manifestation of the disease.
4. a public demonstration, as for political effect.
5. Spiritualism. a materialization.
Manifest:
1. To show or demonstrate plainly; reveal. Ex: “Mercedes . . . manifested the chaotic abandonment of hysteria” (Jack London).
2. To be evidence of; prove.
3. 1. To record in a ship’s manifest.
2. To display or present a manifest of (cargo).
References :