The overflow-wrap or word-wrap CSS property is used to allow the breaking of long strings that would overflow their container otherwise. The typical example is the case of long URLs. Note that word-wrap is just an alias of the standard overflow-wrap.
overflow-wrap acts just in the case of overflow. To hyphenate text use CSS hyphens and not overflow-wrap.
Using overflow-wrap: break-word as a general style is a good idea. The property is inherited and I can't think of any case where you want a long string of text to overflow it's container. Note that overflow-wrap doesn't add a hyphen.
Browser Support: Full support but some browsers still use the legacy name word-wrap. Just include both for full support.
overflow-wrap will be applied to long strings only.
Use word-wrap (an alias used by several browsers) before overflow-wrap for full support:
overflow-wrap vs word-break
The CSS word-break property will break when it reaches the end always, most probably breaking a word, without following language word breaking rules. On the other hand overflow-wrap breaks just long strings. Use just overflow-wrap along with hyphens (which does follow word breaking rules) to hyphenate English and most other languages.