die Veranlassung
reason
The occasion or reason that leads to a specific action or event. Mostly used in formal language.
Ich sehe keine Veranlassung, mich für mein Verhalten zu entschuldigen.
I see no reason to apologize for my behavior.

reason / prompting
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reason
The occasion or reason that leads to a specific action or event. Mostly used in formal language.
Ich sehe keine Veranlassung, mich für mein Verhalten zu entschuldigen.
I see no reason to apologize for my behavior.

'Die Veranlassung' (the reason/prompting) is the noun form of the verb 'veranlassen' (to cause/arrange). When you 'veranlasst' something, you provide the impulse or reason for it. 'Die Veranlassung' is therefore this reason or impulse.
Wer hat den Feueralarm veranlasst?
Who triggered the fire alarm?
The word is especially often used in negative expressions to say that there is no reason for something. The most common form is 'keine Veranlassung sehen/haben, etwas zu tun' (to see/have no reason to do something).
Der Chef sah keine Veranlassung, die Regeln zu ändern.
The boss saw no reason to change the rules.
This word belongs to formal administrative and written language. In normal conversation, one would more likely say 'Grund' (reason) or 'Anlass' (occasion/reason).
Es bestand zu keinem Zeitpunkt Veranlassung zur Sorge.
At no point was there any cause for concern.
The expression 'auf Veranlassung von' is fixed and means 'at the initiative of' or 'on the instruction of'. It is usually followed by a person or an institution in the genitive.
Die Untersuchung wurde auf Veranlassung des Ministeriums eingeleitet.
The investigation was initiated at the instigation of the ministry.
reason / ground
'der Grund' and 'die Veranlassung' can both say why something happens. 'der Grund' is the normal everyday word and works for causes, explanations, and justifications. 'die Veranlassung' sounds much more formal and is often used when an occasion leads to an action. In the fixed phrase 'auf Veranlassung von' (at the instigation of / on the instruction of), it especially means that someone initiated or ordered something. The words can be confused because both have to do with the 'why'. As a practical rule: in normal conversation, you usually say 'Grund'; in official texts or when referring to someone's initiative, 'Veranlassung' is more appropriate.

Auf Veranlassung der Ärztin wurde der Termin sofort verschoben.
At the doctor's request, the appointment was postponed immediately.
Für ihre Absage nannte Lisa keinen genauen Grund.
Lisa did not give an exact reason for canceling.