HP makes it difficult for you to use refilled ink or 3rd party cartridges. This error message is displayed when:
1) You installed a cartridge that has been refilled or made by non-HP manufacture.
2) When your cartridge printed too many pages (>300 for color and >800 for black).
Legally, HP cannot stop you from printing because of a class-action lawsuit ($5 million lost and HP learned a lesson). Therefore, HP made some clever questions:
Click No on this question:
Version 1: If you have just installed the indicated cartridges and you believe they contain new, original HP ink, click Yes. Otherwise, click No.
Version 2: Was this cartridge sold to you as new, genuine HP-branded cartridge that has not been previously used?
If you read the question carefully, then you know that you should click "No". If you click "yes", then HP has the right to stop you from printing.
The correct action is to click "No". Once you select "No", then HP will display another message, and warns you about void of warranty. In fact, using 3rd party or refilled cartridge won't affect your warranty, unless HP can prove that the malfunction was due to the refill (click here for details). As in their own words, "HP's printer warranty does not cover repairs or services due to use of non-HP cartridge or ink". You can click "OK" to dismiss this message and back to your printing
HP will display one message per cartridge, then you can print forever (with the chip usage information turned off).