How does a rabbit learn the smell of a carrot?
Neurons are densely connected: some estimate that the average neuron is connected to 1000 other neurons. Neurons do a simple calculation on the signals sent to them and may or may not send signals to neurons downstream of them.
Complicated processing is done by networks of neurons. These networks are not tidy. A given neuron might be part of many networks. If you colored all the cells in a network, you might find that it overlapped other networks and covered a largish volume not very densely.
Many of these networks are circular in the sense that some of the outputs feed into the network’s inputs. That way, once activated with an incoming signal, a network can use feedback to keep itself active for a while, awaiting further external inputs.
A rabbit will have a network in its olfactory bulb devoted to the smell of carrots. You’ve probably notices how rabbits are always sniff-sniff-sniffing. In the first sniff, molecules from a carrot activate some perceptual cells in the rabbit’s nose. The particular pattern of activation is passed along to the carrot-specific network, which activates and waits. Each of multiple sniffs reinforces the activated network. Eventually, it reaches some threshold and the network sends a signal over to the cortex, where other networks arrange for the rabbit to do something about the smell.
Rabbits aren’t born knowing the smell of carrots. The carrot-specific network is grown (through actual physical changes in cells called Hebbian learning 
) from experience smelling carrots. If the smell has high salience – is associated with the reward of eating – the network grows and strengthens.