I'm sorry, I didn't realize that folks weren't more familiar with Jeopardy!.
Normally if a player is in the lead by more than twice as much as the next closest person (that is, a guaranteed win), he will bet an amount that, if he misses the question and the second-place person answers it correctly, will leave him or her in the lead by a dollar. For example, if Alice has $15,000, Bob has $7,000, and Carol as $4,000, Alice will bet $999. If Alice misses the question and Bob gets it correct, Alice will end up with $14,001 and Bob will end up with $14,000, thus securing Alice the win.
To play for the tie instead, Alice would bet $1,000. Thus if she answers incorrectly and Bob answers correctly, they will both have $14,000. Both win the cash prize instead of the consolation prize(s), and both come back on tomorrow's show. If Alice is hardcore nice, she might even miss the question deliberately (yes, that means she'll be foregoing $2,000 extra in prize money) since that will net Bob $14,000 and she'll be bringing someone into the game tomorrow that she's relatively confident she can beat.
If Alice does not have the game locked up, then normally she would bet just enough so that, if she and Bob both answer correctly, she would end up one dollar ahead. For example, if Alice has $15,000, Bob has $10,000, and Carol has $3,000, Alice would bet $5,001, assuming that Bob will bet the entire amount. If both answer the question correctly, then Alice will end up with $20,001 and Bob with $20,000. If both answer incorrectly, Bob will likely end up with something close to $0, and Alice will end up with $9,999. If Alice answers incorrectly and Bob answers correctly, then unless Bob really screwed the pooch on his betting strategy, he will win and there's nothing Alice can do about it. (Which, incidentally, I have seen before.)
However, if Alice is playing for the tie, she will bet $5,000. That way, if she and Bob both answer correctly, they will both win $20,000, and again, she will carry a player she's likely to beat into the next game.
Obviously, that's not the whole story, because you might adjust your betting strategy based on where the third place person is to ensure that you capture at least second place, and sometimes you tweak the amount so that if everyone blows it, you come out ahead. Or sometimes you might do something irrational if you have some ulterior reason for it; for example, Alice might bet more on the question if it is about 18th Century Authors and she happens to be a literature professor with extensive knowledge in that field. But still, hopefully that paints a good enough picture to understand what "betting for the tie" means, versus trying to win outright.