Let's just start with physics because it's easy. We just talked about gases. Put loads of those particles together, and you can get solids, at the right temperatures and pressures, and you can get fluids. And it turns out that the mathematical equations you use to describe those two systems are different. And the dimension, the simplicity, if you like, the number of terms, in those equations are different [...]. That is emergence. The fact that you have two things, a new state of matter, with properties that wouldn't really seem to apply at the individual particle level, and it has a new language, a new language of description, and a new language of prediction. Those are the two hallmarks.
Now it's interesting you were talking about psychology, advertising, and neuroscience. And that's a beautiful example. Let's imagine that in order to be a really good psychologist or marketer, you had to be a great neuroscientist. Of course a really good marketer doesn't need to be a good neuroscientist. Because all of that detail is a little bit like a particle in a gas relative to a fluid. A good marketer is doing something like fluid dynamics, by analogy. They're understanding collective properties that have their own language. And I think a lot of pseudoscience is where a level that has its own perfectly adequate language starts using the more reductionist language to give it legitimacy.
Life is the most efficient way of returning to thermodynamic equilibrium. Because life is the most efficient generator of entropy. And if you think about what we do when we build factories, what we're essentially doing is turning ordered states into disordered states.
And the cynical answer to your question [what problem life is trying to solve] really is, life is a kind of suicide by the universe.