
die Erklärung
explanation
Information or an account that makes a matter understandable or explains it.
Danke für deine Erklärung, jetzt verstehe ich das Problem.
Thanks for your explanation; now I understand the problem.
explanation / statement
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explanation
Information or an account that makes a matter understandable or explains it.
Danke für deine Erklärung, jetzt verstehe ich das Problem.
Thanks for your explanation; now I understand the problem.

statement
An official, often written, public, or formal comment or statement.
Die Ministerin gab eine persönliche Erklärung zu ihrem Rücktritt ab.
The minister made a personal statement about her resignation.

explanation
The reason or cause for a particular behavior or event.
Es gibt keine vernünftige Erklärung für sein plötzliches Verschwinden.
There is no reasonable explanation for his sudden disappearance.
The noun 'die Erklärung' (explanation / statement) is derived from the verb 'erklären' (to explain). The ending '-ung' turns the verb into a feminine noun.
Kannst du mir bitte die Grammatikregel erklären?
Can you please explain the grammar rule to me?
The verb used with 'Erklärung' (explanation / statement) gives a clue to the meaning. 'Eine Erklärung brauchen' (to need an explanation) points to an explanation. 'Eine Erklärung abgeben' (to make a statement) usually means an official statement. 'Die Erklärung für etwas sein' (to be the explanation for something) points to a reason.
Ich brauche eine einfache Erklärung für dieses physikalische Gesetz.
I need a simple explanation for this law of physics.
In the sense of an official statement, 'Erklärung' (statement) is often combined with adjectives such as 'öffentlich' (public), 'persönlich' (personal), or 'schriftlich' (written). The typical verb for this is 'eine Erklärung abgeben' (to make a statement).
Das Unternehmen hat eine offizielle Erklärung zu dem Vorfall veröffentlicht.
The company published an official statement about the incident.
When 'Erklärung' (explanation) refers to the cause or reason for something, it almost always appears with the preposition 'für' (for), followed by a noun in the accusative.
Gibt es eine logische Erklärung für dieses Phänomen?
Is there a logical explanation for this phenomenon?
reason / ground
Grund names the circumstance that causes or justifies something. Erklärung, by contrast, presents information in a way that helps someone understand the situation. An Erklärung can therefore contain the Grund, but it is the comprehensible presentation of it.

Leas Erklärung machte verständlich, wie der Zugausfall zu ihrer Verspätung führte.
Lea’s explanation made it clear how the canceled train caused her lateness.
Der Grund für Leas Verspätung war ein ausgefallener Zug.
The reason for Lea’s lateness was a canceled train.