Mar 8:12 Why does this generation seek after a sign? verily I say unto you, There shall no sign be given unto this generation.
Notice the contrast of this statement with the previous verse where Christ seems to be offering a sign his muliplication of the bread in feeding the four thousand as a proof of his philosophy.
This verse relates to two similar verses in Matthew, Mat 16:4 (discussed here) and Mat 12:39 (discussed here), though all have very different contexts, all these statements are trigger by religious leaders asking for a sign, but they are all addressed to an entire generation or class of people. The contexts of each of these three verses are very different but those echo each other in interesting ways.
What is particularly interesting about this context of this verse is that it comes right after the miracle of the loaves, feeding the four thousand and right before another discussion about bread and leaven.
The meaning of the Greek word for "sign" that stands out here is the idea of "proof." Proof is in the eye of the beholder. What may have been a sign to those who were hungry for his teaching, meant nothing to those who see themselves as leaders.
If we look at Christ's use of the word for "give," he uses it mostly to discuss the giving of food in parables and the giving of understanding when not talking in symbols. You cannot give people what they do not want. Christ couldn't give people who didn't believe him a sign because they did not want it even though they sought after it.
"Generation" is from genea, which means "race," "family," "generation," "class," and "kind." It is a from of the word that we get the scientific "genus" from.
"Seeks" is from epizêteô, which means "to seek after," "to wish," "to miss," and "to request."
"Sign" is sêmeion, which means a "mark," "sign," or "proof." The word in Greek is used specifically to means a sign from the gods and it that sense, it means "omen," "portent," and "constellations."
"Given" is from didômi (didomi), which means "to give," "to grant," "to hand over," and "to describe."