In the vernacular of the politics of the United States of America, "Balancing the Ticket" refers to selecting a vice-presidential candidate who balances, or gives the appearance of balancing the presidential candidate.
Of course, the vice-presidential candidate has to also be qualified for the job, and hopefully the president will not just be picking a running mate, but someone he actually thinks can run the country. This also relates to the changing role of the vice-presidency, because depending on the time in American history, and the particular administration, the vice-president will also have tasks of his own that may require skills and a personality different than what the president possesses.
In any case, balancing the ticket is a fairly easy thing to do. Write up a list of adjectives to describe the presidential candidate, find their opposites, and you then have an ideal vice-presidential candidate. This is true both of "serious" characteristics, such as the candidates ideology and field of experience, but with slightly less serious characteristics, such as regional background and ethnicity or religion, but even with personal characteristics, such as demeanor.
In American history, the practice of balancing the ticket has been practiced as often as not, although I am personally more familiar with the electoral politics of recent decades. In recent decades we have seen such famous ticket balancing as the boyish, Catholic, Northern John F. Kennedy selecting the older, protestant, Southern Lyndon B. Johnson. Ronald Reagan, a Western conservative governor, picked George H.W. Bush, a moderate party insider from New England. And most recently, Barack Obama, a young black man, picked Joe Biden, who was older, white, Catholic and came from a blue collar background. These are all winning tickets, but most losing tickets were also balanced.
There are also some winning tickets that were not balanced. Bill Clinton and Al Gore were regionally and ideologically similar, and were about the same age. Likewise, George W Bush picked Dick Cheney, a loyalist with a similar background, to be his running mate.
So some unbalanced tickets win, and some balanced tickets lose. A question that could be debated endlessly is whether ticket balancing makes too much difference in the final results of an election. My own feeling is that it probably does not: most politicians spend their time around politics, and around pundits and advisors who spend all of their time thinking about politics. They may overestimate the amount of thought that people put into the intricacies of an election campaign. While a good vice-presidential candidate, who reflects a wide ideological or popular base, can attract some votes, a relatively small percentage of voters would probably base their votes on the real or perceived characteristics of the vice-presidential candidate. Like much in American politics, the idea of "Balancing the Ticket" is a matter of tradition that is probably impossible to verify the effect of. It is another part of politics that is more of an art than a science.