1. A girth for a saddle, consisting of a thick strap secured by passing the end through two metal rings.
2. To get a tight grip on.
3. Informal, to make certain; to secure, or to guarantee.
4. Etymology: American English, "saddle-girth", from Spanish cincha, "girdle"; from Latin cingulum, "a girdle"; from cingere, "to surround, to encircle".

The sense of "an easy thing" is from about 1898, via the notion of "a sure hold".