Basically, upwards causation is that of the action of parts upon some greater whole. E.g. the influence and actions of an individual in a community, causing change in that community (be it good, bad or whatever).
I also explained in detail the role of downward causation: we experience it in everyday life as peer-group pressure, social etiquette, rules, laws etc., all of which go to constrain or influence the behaviour of the parts that comprise a community (people).
But the term upward and downward implies that there is an up and a down, relative to our personal and collective experiences.
As I also explained in Be and Become, the sense of a downward causation derives from seeing reality in terms of a hierarchy -- God (the ultimate authority) is "up there," as is perceived all authority figures being higher, or above us.
All of which comes from a physical survival impetus (animals or people higher than us are of potentially greater threat to our physical survival, if they prove to be not-nice).
And it relates to physical gravity, with "up" giving us a better vantage point to remain safe (in the trees, on top of mountains etc.)
But such perspectives aren't really deeply spiritual, in which "up" and "down" are meaningless. As I've explained elsewhere, there's no hierarchy in the spiritual -- all entities and gestalts are on a level playing field -- we're all able to have faith as a grain of mustard seed and move mountains.
So, I've revised my use of the term "upwards causation", to be a more appropriate and relevant "outwards causation" -- the role of being extroverted, taking action "out there" in the community.
Downward causation is more appropriately termed "inwards causation", in that the constraints or beliefs of the community have an inwards effect upon our (inner) personal dynamics --- what we individually think, do, believe etc. In other words, what goes on internally for each of us is 'caused' by the influence of peer-groups, and various groups in our communities.
So in a fuller 'meta-physical' context, upwards causation is outwards, and downwards is inwards.
That's much more appealing, in that we remove the inference that 'downward' is bigger, or more powerful (e.g. God is more powerful than humans; the government is more powerful than a citizen etc.).
We each have the power to move mountains, so long as we gain sufficient cooperation to do so.
More explained in my article Downard Causation (an edited excerpt of Be and Become)