If something is spinier, it has more sharp points or thorns on it.
Spinier things can be more painful to touch or be around.
Examples:
The cactus is spinier than the flower.
I don't like the spinier bushes.
The spinier plant is not good for hugging.
Ouch! That spinier plant poked me!
The spinier the animal, the more careful you should be around it.
The spinier the better, said no one ever.