IndexedDB was a volatile spec for a year, but has settled down. Chrome, Firefox, Opera and IE10 have shipped it. Safari started to support it in iOS8.
The IndexedDB Polyfill is a polyfill for the IndexedDB APIs over WebSql. This enables IndexedDB to work on browsers that support WebSql. IDBWrapper helps smooth out the cross-browser differences. You may consider falling back to WebSQL when IndexedDB isn't available, but do keep in mind that WebSQL has been abandoned.