All Part of the Magic!
A conductor has many jobs, one of which is expressing her own artistic interpretation of the music to the performers. She knows the composer, his life story, the impetus for writing the music, and even the meaning of the music for the composer; she knows the music itself, its moods, its flow, the story it tells. The performers know all of this too! So it's the conductor's job, ultimately, to herd cats. Each performer is a professional musician and could undoubtedly play solo works for their instrument. But in the orchestra, they must work together. The one to ensure that everyone works together is the conductor and the way she communicates her vision of the music, her interpretive expectations, as well as the basics of tempo and volume and intensity are communicated through body language, facial expressions and the movements of the baton.
As you could see in the example, not all conductors communicate in exactly the same way. This is because conductors have their own personalities and their own takes on conductor as artistic director or conductor as showman. Wild gesticulations can indicate to the musicians a wide open, joyous, raucous, pompous music; it can also signal to the audience "hey! Look at me! I'm all that and a bag of crisps!" Could be enthusiasm for the music or it could be a kind of strutting cockiness.
A final consideration is "who did they learn from?" Chances are good that any conductor you see has borrowed movements, expressions and stances from her own school band directors, from professors, and probably also models somewhat from conductors she's worked with or has seen on stage. She'll take all of those earlier influences and, as time progresses, begin to shape her own conducting style.