In the United States of America, "down ballot" is a term for races for office occuring below the Presidential level. It is usually used in discussions of such things as coattail effects, where having a popular or unpopular presidential candidate at the top of the ballot will affect how other candidates from the same political party will fare. This is mostly in terms of Senators and Representatives, although it would also apply in few states that hold gubernatorial elections in presidential election years, as well as other state wide offices, and even local offices. The effect that a good presidential candidate will have depends from time to time, some people will be more likely to vote along with the party of a popular politician, while others will split their ticket.
The strategies of assisting down ballot candidates forms a large whirl in the already complicated strategy of American electoral politics. Most presidential candidates will spend their time and money in a few swing states, rather than in states that they are either safe or impossible for them. However, because they want to have a congress helpful to their agenda, (as well as personally indebted to them), they will also make some campaign stops in either safe or impossible stops to help various down ballot congressional candidates, through advertising, rallies or get out the vote efforts. Presidential candidates can have a negative down ballot effect too, if they engage in negative campaigning that may alienate people. For example, it could be argued that in the recent election, Sarah Palin's attempts to energize the base to get better turnout in some states caused a negative down ballot effect for moderate Republicans in other states. And this is where the down ballot can get confusing strategically: whether it is better to secure Missouri's electoral votes at the cost of losing, for example, a republican senator from Oregon and a republican representative from Connecticut.
Effect on down ballot races is one reason why election strategies might seem counterintuitive. In the past years, the Democratic Party under Howard Dean has been running the 50 State Strategy, where they attempt to compete in every state. Of course, there is some states that they can't hope to actually succeed in, but in trying to do so, they are building party organizations for other candidates.
Other countries may have a similar effect to the United State's down ballot effect, but it would not work quite the same way in a parliamentary system. which is the most common system outside of the United States.