die Geltung
validity
The legal validity or effectiveness of a law, contract, or rule.
Das neue Gesetz erlangt am ersten Januar Geltung.
The new law comes into effect on the first of January.

validity / recognition
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validity
The legal validity or effectiveness of a law, contract, or rule.
Das neue Gesetz erlangt am ersten Januar Geltung.
The new law comes into effect on the first of January.

The noun 'Geltung' (validity / recognition) is derived from the verb 'gelten' (to be valid / to count). If something 'gilt' (is valid), then it has 'Geltung' (validity). This connection helps you understand the meanings of validity and recognition.
Diese Regel gilt für alle Mitarbeiter.
This rule applies to all employees.
'Geltung' (validity / recognition) is very often used in the fixed expressions 'zur Geltung kommen' (to come into its own; something unfolds its effect by itself) and 'zur Geltung bringen' (to bring out; someone helps something unfold its effect).
Das Bild kommt in diesem Raum erst richtig zur Geltung.
The picture only really comes into its own in this room.
You can recognize the meaning 'Gültigkeit' (validity) from the context. It is almost always used together with formal or legal terms such as 'Gesetz' (law), 'Vertrag' (contract), 'Regel' (rule), or 'Verordnung' (regulation).
Die Geltung des alten Vertrags ist inzwischen abgelaufen.
The validity of the old contract has since expired.
In a legal context, 'Geltung' (validity) is often combined with certain verbs: a law can 'Geltung erlangen' (come into effect), 'Geltung haben' (be valid), or 'seine Geltung verlieren' (lose its validity).
Dieses Gesetz hat seit 20 Jahren Geltung in unserem Land.
This law has been in force in our country for 20 years.
In the meaning 'Anerkennung' (recognition), 'Geltung' is often used with verbs that express striving for or achieving something, e.g. 'nach Geltung streben' (to strive for recognition), 'Geltung erlangen' (to gain recognition), or 'sich Geltung verschaffen' (to assert oneself / gain recognition).
Er hat sein ganzes Leben lang nach Geltung gestrebt.
He strove for recognition his entire life.
meaning / importance
'die Bedeutung' and 'die Geltung' can both have to do with effect, importance, or recognition. 'Bedeutung' is more general and says that something is important or has influence. 'Geltung' more often means that someone or something is recognized, has influence, or shows its effect. In expressions like 'zur Geltung kommen' (to come into its own), it is about something becoming visible or effective. The words can be confused because both can speak positively about importance. 'Bedeutung' fits general importance, while 'Geltung' fits more with status, recognition, or effect.

Am Montag bringt der Lehrer die Ideen der Schüler im Unterricht gut zur Geltung.
On Monday, the teacher brings out the students' ideas well in class.
Aus Zeitmangel haben wir über die Bedeutung des Projekts nur kurz gesprochen.
Because we were short on time, we only spoke briefly about the importance of the project.