The idea is to have one farming planet provide a boost to target population
How is that different from what techs, buildings and specials do for population?
You left out the rest of that sentence and the next one:
The idea is to have one farming planet provide a boost to target population for multiple nearby planets, with the size of the boost depending on the effectiveness of the farmers. A good farming planet could give big boosts to the target population of several other planets.
The current / old system has farming planets that produce food, which gets distributed around to planets to support their population. Lack of this support causes starvation.
The new system has farming planets (or similar) which provide a boost to population capacity of nearby planets. Lack of this boost just means those other planets have their original population capacity; there is no "starvation" (except on planets that have zero capacity on their own) and most planets are basically self-sufficient in "food".
Mostly by convention, techs generally act without with positional dependence like affecting only "nearby planets". Specials generally act only on their own planet, giving a local boost to some stat, possibly including population. Buildings do a variety of things, and I suspect some buildings could interact with the new farming planets to enhance their effect, or could be included in the "or similar" in brackets above.
In terms of how the scripting is set up, and the direct impact, there's not much difference between species, specials, techs, or buildings that can each apply a modifier to population. The distinctions arise from what the player does to get the modifiers, though. For techs, they are researched. For buildings, they are produced. For specials, they are just there, or need to be colonized or captured to be accessible. For species / farming boosts to other planets population, things work mostly like farming used to: you pick a good farming planet, and tell it to farm, and then other planets get a benefit.
The difference now is that the benefit that other planets get is much simpler and avoids many quirks (eg. stockpiles) and annoyances (eg. very unfun "starvation") that arise from food.
I also like that with the new system, it's useful to have more and better farming planets throughout the game. With a food resource system, there's a reduction in its importance and utility through the game... Any more food than necessary to support the population is useless, and as food resource output per planet increases, the need for farming planets would decrease, and additional boosts to farming are less valuable. With the new system, more population should always be useful, and with limited range of effect, additional planets will need to be dedicated to population support (farmings, health boosting, etc.) as the empire expands.
The following makes it sound like you are throwing everything out that previously effected population...
I actually think I made more things affect population directly, because I removed farming and health as distinct meters which were really indirect modifiers of population.
A high population species will produce more of everything in all situations of the game.
Not necessarily, as a) some things give fixed bonuses that don't depend on anything and b) infrastructure may take more of a role as an alternative to population.
What does it mean for a species to have a high population? It can't be about numbers to fit onto a planet.
Higher target population means that for a variety of reasons (which will depend on the bit of content that boosts the target population), more of that species in some not-very-clearly defined sense is present on a planet. That means that things that depend on population do more of whatever they do on or from those planets. What exactly the population number means is likely kept vague intentionally, to avoid issues of comparing "population" numbers of vastly different species. Regardless of the story-interpretation though, the target number indicates the point where the rate of loss equals the rate of birth (or equivalent for that species). By keeping things a bit vague, it's reasonable to have a variety of plausible-sounding things influence what that target population is, including "farming", "health", or "housing" type content.
[...]Population Growth is easy to explain...
Not any more so than target population as the effective capacity of the planet. It's possibly easier to understand why it's useful to have planets get +2 population capacity on them, and how that will impact the game, than it is to understand why getting +5 to a more-obscure growth rate statistic is useful.