To recognize, often formally, that something has been received, usually an item that has been delivered. Jason signed a form to acknowledge the receipt of the letter. Did you get a notification acknowledging receipt of your package?

With evidence of something, especially that which disputes or disproves what someone has said or claimed. I sent Ali a bunch of emails about it, so if she says I never contacted her, I'll come at her with receipts.

To show one evidence of something, especially that which disputes or disproves what they have said or claimed. I sent Ali a bunch of emails about it, so if she says I never contacted her, I'll just show her the receipts.

To (be ready to) produce evidence of something, especially that which disputes or disproves what someone has said or claimed. I sent Ali a bunch of emails about it, so if she says I never contacted her, I'll just come with receipts.

Having received something. The phrase is rather formal and most often used in business settings. Yes, we are in receipt of your resume, and our recruiting team is reviewing it now.