SHE NEVER HAS TO COMMIT TO ANYTHING
For starters, Jigglypuff has a very strong trait (meta knight is the only character who can compare in this regard) in that she is mostly immune to pressure if she wants to be. You can limit the options of almost every character in the game, that's what the current metagame is all about, creating a wall of solid frame data that slowly inches towards your opponent. However, due to her aerial mobility, 6 jumps, Pound and solid aerials Jigglypuff can escape all pressure by jumping and just holding a direction (air dodge is sometimes necessary). This gives her a free ticket to the ledge or basically anywhere on-stage. This isn't just a tool she has from neutral, mind you, she can jump into the opponent - close enough to be a threat via bair/pound/grab - and then just safely drift away. This lets you work out your opponent's habits, get inside their head and even condition them (to some degree, it by no means supplies her with all the information she needs).
BASIC PRESSURE
Secondly, she actually has some pretty strong tools just for general use, especially on the defensive side of things. I can't go through every single situation of course, but the general idea behind her spacing game is to jump into the very tip of bair range - from there she can mix-up by just fading away (as mentioned above - which can in turn be 'canceled' into a B-Reverse Pound, but I'll cover Pound later), she can jump again which opens up a whole new web of options (fade away + falling bair is very strong from this height, you can cross them up pretty easily, etc... Too hard to go into everything lol), she can go straight through the opponent (high risk, high reward), she can obviously just bair which is a decent move (and because she retracts her leg after using it, it's safe despite lacking a prominent disjoint), etc... It might sound like the opponent can just swat her out of everything on reaction, but she is actually intimidating enough to force opponents to throw out moves, this GIF paints a very good picture of how her spacing game works imo:
(That was from way back when I had a bad air dodging habit, but you get the idea - especially note how the DK shields after I hit him the first time, he could've just swatted me out of my jump into his face but he was afraid of throwing out another move; I'll get into Puff's punish game in a sec)
Jigglypuff is VERY good at the fundamentals of spacing (moving just into your opponent's range, and then moving just out of it), and her air speed lets her punish mistakes like that better than a lot of people think. I utilize dash-dancing and pivot-walking a lot with her because being in a specific position at a specific time is incredibly crucial to her playstyle, and her air speed + floatiness lets her do it really easily. She can also mix-up her standard backwards-facing-short-hop approach with a forward-facing SH nair - because it's a sex kick and because puff is so mobile you can often drift into the opponent and hit them out of their jumps when you get the read.
Long story short, her aerial mobility + a few key moves give her the tools to handle anything if you're smart enough.
PUNISHING
Her punishment game is phenomenal, her aerials just string together beautifully, she can land wherever she wants after a hit giving her an insane amount of options that the opponent has to deal with. This is one of the main areas that I feel the American Puffs are lacking in, but she can easily get 30% every time she hits in some match-ups (marth springs to mind). If you need an illustration of this, just think about all the things I could've done after that bair hit in the GIF - I could have landed closer to him (in grab range for me), jumped again (from there I have a billion options yet again), landed far away (as I did) and then go through him with a cross-up (I instead decided to just jump into his range to gain information, which I mentioned above), I could've predicted a spot-dodge/dropped shield/OoS action after I jumped into his shield at the end and B-reverse Pounded it, etc...
Her option coverage off of a single hit is just amazing.
Then you have her back throw. Back throw near the ledge sets up so beautifully for everything against some characters I can hardly put it into words. It creates reliable gimps in some match-ups - very few other characters in Brawl can say that, but it really just puts them at this perfect angle that very few characters are happy being in against Puff (above and behind her, but with no option of retreating and the added risk that anything that hits you will put you further off-stage, but still in that awful position). All of her throws are amazing for setting up/continuing pressure/strings to be honest, they put the opponent in bad positions and she can limit their options heavily just with her usual jump-into-the-opponent shenanigans.
Then she has Pound. Pound seems like a super nooby move because of how slow it is on start-up and cool down, but bare with me here: Pound is amazing because it has a large, long-lasting hitbox that moves. That's basically all there is to it, when your opponent commits to something you can time/space a Pound so that it hits the opponent as soon as they are vulnerable (this is why the b-reverse is important, it has better distance). On top of this, you also get a lot of situations with Puff where you condition them into thinking you'll drift back out so they won't commit to ANYTHING (including shield, shield is a commitment vs. a character who can cross-up and has a good grab + other options) and then you just Pound their face - that sounds especially nooby, but trust me, it's legitimate.
Finally, there's Rest. Rest is amazing because it's a frame 2 (practically frame 1 because the first frame is invincible) KO move. At KO% I legitimately create pressure on my opponents just by jumping around their shield because a single misstep and I can be inside them and out-speeding all of their options. You know how grabs sometimes get spot-dodged? Rest. Throw the opponent, jump into them to force a response and read it? Rest. Something I've been toying around with recently is grab-releasing at high % (on the ground) and then just doing that "hover over their shield with the threat of rest" thing.
I really don't like how people write it off as a "high risk, mid-reward move" because you shouldn't be using it if it's a risk, it's not like you have to start charging it preemptively or something, you see they are vulnerable and you take that opportunity to get inside them, THEN if they commit to something you can rest - the best punish they'll be getting out of you 'going for a Rest' is just hitting you away before you hit the button, not a fully-charged smash attack while you are helpless.
TIME-OUTS
The final thing to mention is her time-out ability. There isn't much to say here:
1. Six jumps, amazing air mobility, pound - she can waste a lot of time in the air
2. One of her stereotypical problems is a terrible approach - this doesn't matter if she doesn't have to approach.
That's pretty much it, I don't think her ability to time people out has ever been contested much.
It's worth noting, though, that a time-out style where you still pressure your opponent to some degree and attempt to hit them is superior to one where you just try to avoid everything - with our current stage-list, no character can play a keep-away game without throwing out attacks of their own, and Puff is no exception.
