Lambda functions have been introduced to improve code terseness and encourage functional programming practices.
You do not have to use them at all, but they are quite awesome for turning multiline function statements into single lines of code. They are very useful when using functional programming methods such as map, filter and reduce.
Like any language syntax, they are only cryptic if you do not understand them. The Spread (...) syntax is another amazing ES7 feature that drastically improves the ability to interact with arrays and objects.
In terms of compatibility, most people writing ES6/7 code are still using transpilers like Babel together with polyfills. Unless you are 100% sure all of your code will work in all browsers, you should be doing this too.
All this being said, the ES6/7 features really start to shine when used in a fully modern JavaScript development environment where import and export as well as all modern methods are supported. I encourage you to try out a boilerplate like create-react-app or something similar where you can play around with the new version of the language, it really is almost a completely different language to what it was 5 years ago.