'Big picture' to me means a range of things such as seeing productive advantages & emergent situations, and thinking multi-contextually with creativity & erudition.
Scenario #1: Productive advantages
A couple of people find a wallet on the ground filled with dollar bills amounting to hundreds if not thousands. One of them wants to spend it all on immediate gratification such as drugs, a fancy wardrobe or media consumption. The other one makes the point that they could invest the money in activities/objects that would return even more money or more gratification than one-off options.
Here big picture means seeing all off the possibilities and judging which ones are most productive rather than what's most immediate to one's desires. Investing in drugs rather than buying them, suits and other attire to impress future associates, or a quality entertainment system are ways that could still be big picture even if focused on a material lifestyle.
Scenario #2: Emergent situations
A plane crashes into the ocean halfway through its trip. The remaining survivors make it to an uncharted island. They form groups among themselves and follow their own plans for survival; all but one of the groups spend their time trying to fish and collect coconuts, the group instead looks for safe shelter expecting the island to become hostile during the night, realizing they can live for awhile without food. Nighttime comes and the other groups realize they have nowhere to rest and sleep, ferocious animals come out and attack them all.
Seeing the emergent situation rather than the immediate, current situation is another example of the big picture.
Scenario #3: Multi-contextual thinking
A traveler comes across a bridge blocked by a mythical creature. The creature tells the traveler its riddle must be answered correctly in order to pass. "What goes on four legs in the morning, on two legs at noon, and on three legs in the evening?" The traveler thinks 'that's impossible, no creature does that'. After a long period of intensive thinking the traveler begins to wonder what the creature meant instead of just what it said, and realizes the riddle is only impossible in literal reality. The traveler proceeds to play with the meanings of 'leg' and time of day.
Big picture here means using critical and creative thinking instead of following familiar or simple lines of thought.
Scenario #4: Erudite thinking
A party of explorers discover an ancient artifact atop the tomb of a king, its respective culture's language is inscribed. One of the party members, the erudite, observes the artifact and interprets the message to be a curse to all intruders who come to raid the tomb. However the erudite knows through extensive research that the curse is activated by stepping on one of the tiles near the exit of the chamber, which would block the exit and release scarabs.
In this example, big picture means using a wide body of knowledge to understand the meanings and implications of a situation, instead of seeing a situation for what's only presently available to the senses.