We picture intelligence principally, as being able to make accurate predictions, especially as regards problem solving. At the point a complex self-model with intentions can be held in mind (rather than just bodily awareness, proprioception etc) something interesting happens, a feedback loop. If you decide to be this kind of person: you can expect such & such outcomes; if another kind: different outcomes - instead of simply predicting outcomes of actions, adjusting the self-model (character, superego, etc) can change future sets of possible outcomes, and imagining future outcomes of a way of living, can inform how we choose to live. This level of self knowledge is the beginning of choosing how to be, who to be.
To support this, I'd look to Dunbar's Number & how human intelligence seems to have emerged mainly for navigating our social landscape & intentions of others, rather than mainly problem solving (like cephalopods & corvids which are solitary or have small social groups). We jumpstart our learning by mirroring others, using specialised 'mirror neurons'. Looking for intentions, and mirroring behaviours, which gives us intersubjectivity: projecting ourselves into the situation of others, because that helps predict them - and, causes us to need to understand our own intentions, and go beyond mirroring into true understanding of physical activities (chimps who don't creche-rear young seem to have less mirror neurons, and struggle to learn by imitation in adulthood). These are also feedback loops, as illustrated in the Buddhist metaphor Indra's Net.
So, having a self-model which can be changed through volition, is key to being truly responsible for your volitions, and character; to moving beyond conditioning by experience and biology like a meat-robot. Feedback allows novel and unpredictable emergent behaviour to occur, in complex systems of all kinds.
The most compelling model for minds to me, is Hofstadter's strange-loop idea, where feedback loops that include self-models in the way described are crucial.
I go into more detail about the themes and approaches mentioned in this post here
According to the major theories of concepts, where do meanings come from?