Let's pretend for a moment that the body is completely democratic, that electrical signaling does not exist. Each cell can communicate with every other cell adjacent to it. Let's say we're manual therapists, working on somebody's toe. Let's say the cells in the patient's toe can "feel" us just fine, and they want to tell all their little friends about our contact. They do this through squirting molecules out into their extracellular environment, hoping that one or more of the molecules will land in an appropriately shaped pocket on some other cell's membrane, that the recipient cell will pick up the phone (accept the molecule), receive the news, be perturbed about it enough to care, and respond somehow, maybe by passing the message on.
Let's pretend this happens from cell to cell. But like one of those games where messages are passed around a room, by whispering in the next person's ear, the message soon becomes garbled and by the time it gets all the way around the room it's often not the same as when it started out.
In the body, the message gets passed along for a few cells out, maybe, but it will degrade, fade, dilute. We're talking chemistry in an ocean, really..
So, neurons evolved! Problem solved! Message stays crisp, each neuron responds to a particular sort of stimulus. Hi-fidelity occurs. There are only three cells between anywhere on the surface of the body, and a part of the same body which can protect its organism! The ENTIRE organism! How cool is that!?
Some of the neurons that evolved, and live up in ganglia by the spine, grew two enormously long arms, one of which monitors the skin on the outside of the toe, and the other goes right into then up a pathway at the back of the spinal cord - right up to inside the medulla! [dorsal column nucleus] Which makes these the longest cells in the entire vertebrate body!
There are still places where molecules have to swim across oceans, but only two places, and they are special enclosed places called synapses, with lots of helpers available called synaptic proteins, to help the message remain non-degraded. Yeah, sometimes problems happen and messages go astray or maybe the organism hasn't got quite a full complement of messenger molecules, or is lacking a particular dock shape.. but on the whole, information is greatly sped up, and action can be taken well ahead of danger to the organism, usually.
Single cell organisms still have to do everything on their own, with only a membrane between them and the rest of the entire world; some multicell creatures without neurons still have to rely on cell to cell communication. Life is way better (at least faster in lots of ways) than it used to be, since evolution came up with the neural internet.