What if electricity didn't exist?
Well, the universe literally would not exist as we know it, because electricity is streams of electrons, and without electrons, compounds (and thus most matter) wouldn't exist.
If electricity (electromagnetism) did not exist the universe would not exist, since EM forces are an integral component of the (commonly accepted) standard model.
What if humans didn't know how to use electricity?
We didn't know how to use it for most of our history, so I imagine we'd revert to a mid-1800's society, where machines were steam powered and we had to read for personal entertainment.
We wouldn't be able to watch TV, go on the computer, talk on the phone.
We'd have to play games outside, and use our imaginations more, like they did in historical times.
Parents wouldn't be able to punish by taking away computers or cell phones because neither would run anyway.
Imagine cold showers or baths; no microwave; no cold drinks in summer; even worse no air conditioning and no cars (Cars need electricity to run the fuel ignition system.)
One could heat water on the stove (probably a wood stove, hot, sweaty, and smokey, why many old kitchens were walled off from the rest of the house). But, you didn't prohibit using Natural Gas for Hot water, or for the stove. One can even run an absorption refrigerator on Natural Gas or Propane, or anything that would run a compressor could run a freon based refrigerator. With a little imagination one could use a solar hot water heater too.
Transport would be steam-driven, animal-driven or human-powered. You'd have a bicycle, a horse-drawn carriage or you'd just walk everywhere you went, and you'd go long distances by train. By now someone would have invented the horseless carriage, which would run on either a small boiler or maybe a diesel engine--diesels don't need electricity to run, and you can rope-start them if you have to.
Remember the old cars had cranks out front. You'd get outside