When considering the factions primarily (but also some other elements in the game) I see things like '+1 planet' or '-1 police' and so on. Trouble is, I have no idea what any of that actually means in the context of the game. I can't judge the significance of their benefits or downsides, and I'm having difficulty finding a precise explanation. Thanks for any help in advance.

You helped very much, thanks. Social Engineering gives me much better control over my faction, and I have a greater understanding of what the faction bonuses do.

It is a vital part of the game, at first when I started playing I really ignored it until I saw that the different policies can really have a great impact on your faction.

Adapting them to your current needs and fiddling around with them is great fun and provides a good challenge. Check some FAQs about the different factions and their advantages/disadvantages.

Something to note is that the bonuses seen in the social engineering screen also apply to individual bases, where they can be further enhanced with base facilities. This can lead to some very powerful strategies if you know how to work the system. For advantage, one such strategy is boosting Growth to put your cities in a permanent state of population boom early in the game (pop boom means a city grows by one population each turn, so your cities grow in size, and production, extremely rapidly). For this strategy a city needs +6 Growth (along with +2 or more nutrients, which is controlled by which squares the city works). Choosing Democratic and Planned in social engineering will give you +4 Growth for all bases, then building a Children's Creche in a base will give another +2 Growth for that base for the needed +6 Growth- and just like that the population at that base takes off.

Something to also note is that you can use specific secret projects to cover for areas in social engineering that you may specifically choose to neglect. For example, I like to play as the University, which starts with -2 Probe, and some of the social engineering choices I like also give penalties to Probe. Normally this would present a problem, but by making sure I build the Hunter-Seeker Algorithm I become immune to all probe team actions, so I can afford to have -4 (or worse) to Probe without suffering much in the way of real penalties.