another thought; distraction
Almost exclusively used in the set phrase 余念がない, meaning 'to be completely absorbed in something with no room for other thoughts'. Rarely appears outside this negative construction.
He was completely absorbed in his research.
The children are totally engrossed in their play.
He is completely absorbed in researching cooking every day.
一心不乱 is a more literary na-adjective/adverb meaning 'with undivided, single-minded attention', whereas 余念(がない) is the everyday phrase for the same state of total absorption.
集中する is the common, general verb for 'to concentrate', while 余念(がない) specifically describes having no room left for any other thought while doing something.
Compound of 余 (extra, remaining) and 念 (thought, sense). The literal meaning is 'remaining thought', which developed into the idea of having no other thoughts when used in the negative.