To buck up is to behave like a buck - in the sense of, a male deer - that is rutting, that is, in the midst of its mating cycle. This would be similar to a cat in heat, except it applies exclusively to males and represents aggressive male behavior, such as butting heads with other bucks (figuratively and very much literally), displays of antlers to female deer, and so forth.
This expression has evolved from a meaning similar to "dressing up" (that is, dressing in a snappier/ more vibrant manner that is pleasing to women) to the sense of "raise your spirits" and to become more enthusiastic. However, there is another connotation. Let's begin with an example.
Example: In reference to disappointed Democratic Party and left-wing political activists, Vice President Joe Biden revised an earlier comment in which he told people to "stop whining" with the following statement:
"And so those who don't get -- didn't get everything they wanted, it's time to just buck up here, understand that we can make things better, continue to move forward and -- but not yield the playing field to those folks who are against everything that we stand for in terms of the initiatives we put forward," Biden said on MSNBC.However, in this sense, "buck up" is really telling people to "man up," to behave with a strong, male spirit, to show some backbone, and indeed, to grow a spine.
Thus, it is difficult to understand his comment as an attempt to tell Democratic activists to stop whining, just as he had done before. VP Biden simply used an older expression to convey an identical message without using the same words in the belief that people would find "buck up" to be less offensive than "stop whining," even while conveying the exact same message: that left-wing activists should rise up and vote for the Democratic Party in the 2010 mid-term elections.
Thus, it is a distinction without a difference. Indeed, younger activists may not even understand what "buck up" is intended to mean. Men in their late 60's who have been involved in politics for most of their lives certainly would know the term, however. We cannot know if those in the intended audience who are familiar with the term will understand the message as being any different (that is, less patronizing) than the earlier "stop whining" statement.
P.S. Telling any American adult to stop whining is to treat that person like a child and is normally considered rude to the extreme.