According to the dictionary, "intelligence" means "capacity for learning, reasoning, understanding, and similar forms of mental activity". Since it's a "capacity" sort of thing, there is therefore a range of intelligence, with some having more capacity than others.
Sometimes that range is compared to a threshold, usually arbitrary, above which the person or thing is considered intelligent. For example, we might say, "she's intelligent but he's dumb as a rock", which just means that she exceeds some arbitrary level of intelligence, but he doesn't. This assumes that a rock has zero or very limited intelligence (which may be a bad assumption given that silicon can be considered a type of rock).
When we consider the possibility of extraterrestrial intelligent life, we also compare it to a threshold. We'd rather expect that the life, to be considered intelligent, can communicate, builds stuff, and probably lives in fairly large groups. Of course, an ant colony qualifies as an intelligent life form by that description, and I've often wondered if aliens visited the planet, if at first blush, they could tell the difference between the intelligence of ants and the intelligence of humans. We both scurry about, build stuff, communicate, have some understanding of the world, and act on that understanding to extract resources from the world to raise our young.
One can argue that ants don't actually "understand" anything. They're just little machines and their behavior is completely emergent due to their simple "programming" interacting with the world. That's true, but the same thing can be said of humans. We're just bigger machines and our behavior is completely emergent due to our somewhat more complicated "programming" interacting with the world. I believe that's also very likely to be true.
Let's look at it incrementally. Humans certainly have "capacity for understanding". How about other primates? I'd say certainly. Cats? I'd still say certainly, but they're less intelligent than primates. Mice? Well, they certainly seems to understand that it's a bad idea to hang out around cats, but they're less intelligent still. Ants? I'd say an ant understands its world in a primitive way, but here we get to that arbitrary threshold thing where some will agree with me and some won't. Roundworms? I think most would say no. Rocks? No.
By the above sequence, the level of intelligence according to an observer is clearly very closely related to number of neurons. A roundworm has 302 neurons, an ant has about 250,000 neurons, a mouse has 75 million neurons, a cat has a cool billion neurons, a chimpanzee has two billion neurons, and a human has 85 billion neurons.
A neuron is a neuron is a neuron, regardless of species. The more neurons, the more intelligent. Intelligence is an emergent phenomenon from the activity of those neurons. There really is no objective threshold that demarcates intelligence from non-intelligence or understanding from non-understanding (for example, you can't say any species with more than 97,423,014 neurons is intelligent, those with less aren't).
Intelligence for biological entities is all simply a matter of degree based on the number of neurons.