invest: to use, give, or devote (time, talent, etc.), as for a purpose or to achieve something.
As I've been digging through old AD&D books, Labyrinth Lord, and even LotFP to reacquaint myself the way things used to be. Comparing 4e to 0e or 1e, I think I've hit upon an important difference that forces players into one mindset or another - investment.
In 4e, the DM designs an encounter, follows the rules and formulas for force strength and treasure packets. WotC has made it quite easy to create a well balanced encounter, and it's pretty comfortable to use.
When the players get to the encounter, the DM describes what is there, pulls out a map on paper or vinyl or some tiles, positions everything correctly and sets up the monster minis. Then the DM has the players put their PCs down in a specific place, and the players analyze where their minis should go as to be most effective for the set-up, etc. The order may differ, but time and thought go into both sides of preparing for an encounter.
Then the DM says "Roll initiative." Wham. The DM is invested. The players are invested. They are going to what thy are supposed to do - which is fight and maybe do some sort of skill challenge while fighting. It's all laid out right in front of them, and it took some effort.
In many ways, this is railroading. It's a welcome railroading, I've found, as players know what is expected and know that the DM has used all those little balancing formulas and the whole game is designed so that they will most likely win, they just need to pay attention and not blow too many rolls.
The old way was that the DM came up with an idea for an encounter, then during the game, described the situation and asked "What do you do?"
There was no investment. The players then could then do whatever they wanted. They could try to engage in a conversation with a bugbear. They could run away screaming. They could even draw their sword and fight. There was no apparent investment by a DM into any particular outcome, so the players never felt pressured in doing any particular thing except surviving and grabbing loot - or whatever else took their fancy.
Nothing was expected. No little toy soldiers were lined up for war. No battle lines were drawn. It was just "What do you do?"
Maybe I'm exaggerating and simplifying, but I do think that if you are invested in an action, you are more likely to complete that action to it's end. So that is my big thought of the day. :)