New Year's resolution
A goal or intention set at the start of the new year, often declared in January.
My New Year's resolution this year is to exercise every day.
Making New Year's resolutions is easy, but keeping them is hard.
抱負 means 'aspiration' or 'ambition' in general, while 新年の抱負 specifically refers to a New Year's resolution.
Compound of 新年 (new year) + の (possessive particle) + 抱負 (aspiration, ambition). The phrase is a calque from English 'New Year's resolution' and became common in modern Japanese.