Intrinsic motivation is commonly categorised as motivation that comes from within an agent, and is not linked to any external structure of reward or punishment. This seems straightforward but is a bit more complex than first sight because we need to analyse what is left if we take away external reward and punishment.
Human beings in general appear to be wired to derive satisfaction and enjoyment from engaging in exploratory behaviour engaging with our environment. This mental system is linked to the other systems you've developed as an individual and has as an output, all of the behaviour you're intrinsically motivated to do, because you flow, or find satisfaction or enjoyment in them. Like walking in the countryside, or writing.
Intrinsic motivation is generally regarded as more reliable than extrinsic motivation. I have a sneaking suspicion that the two types of motivation are often mixed in some ratio.