A disclaimer means no rights are claimed to the word disclaimed except in the way the applicant uses it.
About 1/2 of all TM applciations get rejected, probably because so many applicants try to do it themselves, or do it with an advice-free service like Legalzoom, and without understanding the process and the strategies, chances of failure are pretty good. If you're planning on applying for a TM, increase your odds by hiring a lawyer, it's a good investment.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
When a trademark owner disclaims in its trademark registration a portion of the trademark, the trademark owner is declaring to the world that it claims no exclusive right to use that disclaimed portion apart from the trademark as a whole.
So ... by registering Ring Pop as a trademark with Pop disclaimed, the trademark owner claims the exclusive right to use the Ring Pop phrase to brand its product or service but disclaims the exclusive right to use Pop by itself to brand that product or service.