넘기다 is passing something over — and figuratively, letting a moment pass rather than making an issue of it: 그냥 제가 참고 넘겼던 것 같아요 'I think I just held it in and let it go', 안 물어봤으면 모르고 넘길 뻔 'if he hadn't asked we'd almost have let it pass unnoticed'. The -고 clause is what you did instead of reacting, often a quoted brush-off: '괜찮아' 하고 넘겼어야 됐는데. The literal sense is also here: 하나씩만 먹어보고 넘기자 'one bite each, then pass it on'.