absegnen
to approve
Colloquial for giving official agreement or approval for a plan or undertaking.
Der Vorstand muss das neue Budget nur noch absegnen, dann können wir starten.
The board just has to approve the new budget, and then we can start.

to approve / bless
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to approve
Colloquial for giving official agreement or approval for a plan or undertaking.
Der Vorstand muss das neue Budget nur noch absegnen, dann können wir starten.
The board just has to approve the new budget, and then we can start.

'Absegnen' is a separable verb. The prefix 'ab-' is placed at the end of the sentence in a main clause. In a subordinate clause or infinitive with 'zu', the verb stays together.
Meine Chefin segnet den Urlaubsantrag hoffentlich ab.
Hopefully my boss will approve the vacation request.
The word consists of the prefix 'ab-' and the verb 'segnen' (to bless). The prefix 'ab-' gives the word the meaning of 'abschließen' (to complete) or 'fertigstellen' (to finish) here. So one gives one's 'Segen' (blessing) in order to bring a matter to a close.
Sobald die Pläne abgesegnet sind, beginnen die Bauarbeiten.
As soon as the plans have been approved, construction work will begin.
The meaning 'genehmigen' (to approve) is colloquial. In formal or official texts, this word is generally avoided.
Kannst du kurz meine E-Mail absegnen, bevor ich sie verschicke?
Can you quickly approve my email before I send it?
Whether the colloquial or the religious meaning is intended is easy to recognize from context. In the office, in politics, or in project planning, 'absegnen' always means 'genehmigen' (to approve). Only in a church context is the religious blessing meant.
Der Stadtrat hat den neuen Bebauungsplan abgesegnet.
The city council approved the new development plan.
to reject
'ablehnen' and 'absegnen' form an opposite pair when it comes to plans, suggestions, or decisions. 'ablehnen' means that someone does not give approval. 'absegnen' colloquially means that someone officially or semi-officially approves a plan. 'absegnen' often sounds as if a person in charge only still needs to give their okay. The religious meaning of 'absegnen' is not meant here.

Der Chef segnet das neue Konzept vor der Präsentation ab.
The boss approves the new concept before the presentation.
Die Leitung lehnt den Urlaubsplan für diese Woche ab.
Management rejects the vacation plan for this week.