I think the paredit stuff is a bit overblown but apart from managing parens for you, another simple example is editing single expressions. e.g. in Java you might have a line: "int a = blah.bar(something, thing, whatever);" If you realize you need to actually pass "whatever" first, not last, unless you know an IDE shortcut that can make the edit for you, you're going to have to type stuff. I would probably just move my cursor to the start, type "whatever, ", move my cursor to the comma after "thing" and highlight to the end then delete. If "whatever" was a longer variable, or even more interestingly an entire sub-function call like "whatever(x, y, z)", I might instead highlight it all, cut, backspace the comma, move cursor to the start, paste, type a comma. Moving the cursor to the start might be character by character, or using the operating system wide ctrl+left/right to move in 'word' chunks, or possibly it's faster to use the 'home' key first or god forbid the mouse. Oh no, I might miss a comma or somehow mess up a paren/semicolon or typo a name?! Whatever, it's rare for me, and for most mistakes I'd get a red squiggly alerting me to it immediately. I like typing, and prefer most 'helpful' plugins get out of my way for most things, so such a process isn't that annoying to me.
But I do at least see there's a nicer process if you have something like paredit: you just move you cursor to the "whatever" (even if it's instead "whatever(a,b,c)") and a command will move it to the left/right/etc. and fix up anything that needs fixing up. In Lisp though the base syntax is so simple and uniform that there's not usually much needing "fixing up" -- there's no pesky commas to deal with for instance, and having the opening paren come in front of the function name instead of after simplifies a lot of things. The worst is adding/removing/moving a form that's at the end of a let binding, or sometimes introducing a let binding, or sometimes adding something to the end of a function that previously ended with ))).
I like to use vim (which does have paredit though I have it disabled) and just having the ability to jump between open/close parens by pressing "%" and to cut jumps as a whole, or the insides, without having to move my cursor character by character, is good enough for me. I still use some paredit-like commands in some instances like moving forms around or in those "worst case issues" I mentioned but I use them with these mappings: https://github.com/tpope/vim-sexp-mappings-for-regular-peopl...
There are more advanced things but how much I care about them varies; I don't tend to need them for Lisp, though every so often I'll miss something from Eclipse that I suspect not even emacs does (or does well). e.g. I know emacs can do a "templateized" completion just like a Java IDE where you type a function name and it completes it and inserts its required arguments as placeholder variables to later define/type over, I don't know though whether emacs can then let you place the cursor over each one in turn and with something as easy as 'ctrl+1' hoist that var to an assignment form just above (I did this all the time in Eclipse to avoid having to choose a name, type it, and type its correct type). (In Lisp it's complicated by needing to introduce a let binding if it doesn't exist or append to one if it does. It wouldn't surprise me if paredit can do this, it's just that I'm aware of some refactoring tools in Slime but they don't tend to approach what Eclipse or IntelliJ users expect even if in theory they could.)