1Of cloth or stitching: to come apart, split open along a seam, or start to tear. Also used figuratively of a defense, an organization, or a plan giving way at its weak point. The godan verb ほころぶ covers much the same ground; this one is ichidan, conjugating ほころびた / ほころびて. Usually written in kana.
古いセーターの袖口がほころびてきた。
The cuff of my old sweater has started to come apart.
鞄の縫い目がほころびて、中身がこぼれ落ちそうだ。
The stitching on my bag has come apart, and the contents look ready to spill out.
何年も着ているコートのポケットがほころびたので、母に直してもらった。
The pocket of the coat I have worn for years came apart at the seam, so I had my mother mend it.
終盤に入って、チームの守備がほころび始めた。
Going into the final stretch, the team's defense started to fall apart.
2Of a bud or blossom: to begin to open. It captures the moment of just starting to bloom rather than being in full flower, and carries a slightly literary, seasonal flavor.
梅のつぼみが春の日差しにほころび始めた。
The plum buds have begun to open in the spring sunlight.
桜のつぼみがほころびるのを、毎年心待ちにしている。
Every year I look forward to the cherry buds starting to open.
庭のバラが一輪、朝の光の中でほころびていた。
A single rose in the garden was opening in the morning light.
3To break into a smile; for one's face to soften into a grin, usually without meaning to. Most often seen in the set phrases 顔がほころびる and 口元がほころびる.
孫の写真を見て、祖父の顔が自然とほころびた。
Looking at the photo of his grandchild, my grandfather's face broke into a smile.
娘の一言に、思わず口元がほころびた。
At my daughter's remark, I could not help breaking into a smile.
合格の知らせを聞いて、彼女の表情がほころびた。
When she heard she had passed, her expression softened into a smile.