means A firm decision to do or not do something, or the act of settling a problem, dispute, or question with finality.

from From Latin 'resolutio,' the act of loosening or untying, from 'resolvere' — 're-' (back) plus 'solvere' (to loosen, release, dissolve, the same root that gives us 'solve' and 'solution'). The original sense was literally a coming-apart: dissolving something into its parts. From there it drifted toward the mental act of breaking a hard question down until it 'resolved' into a clear answer — and finally toward the firm-minded decision you reach at the end of all that loosening. So your January vow shares a bloodline with melting and dissolving, which feels about right for February.