Is the second defined arbitrarily? According to the definition a second is defined as the 

duration of 9,192,631,770 periods of the radiation corresponding to
  the transition between the two hyperfine levels of the ground state of
  the cesium-133 atom.

Why specifically 9,192,631,770? Is there a scientific purpose for such? 
And if there is a scientific purpose, why is this method (cesium atomic clock) the most accurate for it?
 A: The practice of dividing the degree used to measure angle into sixty minutes of arc, and that into sixty seconds of arc is over 2000 years old. The corresponding practice of dividing the hour used to measure time into sixty minutes, and that into sixty seconds, is over 1000 years old. Why sixty? That's over 5000 years old. The Sumerians and Babylonians used base 60 arithmetic.
Old practices die hard. In the case of angle and time, they haven't died yet. The French metric system promulgated in the late 18th century worked fantastically for mass and length (and related concepts such as area and volume). One key factor in this success is that there were no standards for mass, length, area, and volume.
The French also tried to metricize angle and time; there they failed. Old practices die hard, particularly when they are very well standardized. We still use degrees, minutes, and seconds to describe angle, and hours, minutes, and seconds used to describe time. Given that there are 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute means there are 86400 seconds in a day.
The success of the meter and kilogram and the failure of decimal angle and decimal time taught early metrologists something. When no standard exists, make one up. When a standard does exist, it's best to follow it. Now that we have well established standards for everything that is physically measurable, meteorologists follow the second rule. Redefinitions of a standard are always consistent with previous definitions. For example, the definition of the meter has changed multiple times. The current definition appearing to be completely arbitrary. It's not arbitrary. It's consistent with the initial definition of the meter.
The same goes for time. While the definition of a second has been refined many times, it has always been done in a manner that is consistent with the thousand year old concept that a second is 1/86400th of a day.
A: It's historical.  The second was originally defined so that $60\cdot 60\cdot 24\,\rm s$ added up to a solar day.  But that's a little hairy to measure, because the length of the day varies through the year.  The sunrise-to-sunrise time varies from winter to summer.  The noon-to-noon time interval, which would be operationally defined as the interval between solar meridian crossings, also varies through the year due to the eccentricity of Earth's orbit around the sun; the pattern it makes is called the analemma.  So practically the second was historically defined so that $60\cdot 60\cdot 24\cdot 365.25\,\rm s$ adds up to a year. And just to be precise, the original SI definition of the second was that it was the appropriate fraction of the year 1900 — nice and specific, but not repeatable.
With this definition of the second, several new facts about nature were discovered:


*

*There is an easy-to-define atomic transition between electronic excited states in cesium atoms with a frequency close to 9.2 GHz.

*This frequency only depends on basic facts of nature, like the strength of the electromagnetic force and the masses of the electron and nucleons.

*The rotational period of the Earth actually isn't all that stable. For example, a big earthquake, which moves a lot of rock by a (geologically) small distance, changes the Earth's moment of inertia and the length of the day changes to conserve angular momentum.  I dimly remember that the Christmas earthquake in 2004 lengthened the day by 5–10 μs, which changes the length of the day in the tenth significant figure.


With the invention of the cesium fountain clock, we had a better frequency standard than the rotation of the Earth.  So the best value for the transition frequency of this clock, in units of the prevailing definition of the second, was arbitrarily taken to be "the" second.
There is a similar transition planned for 2018 to define the kilogram in terms of the current best values for several fundamental constants.
I have heard murmurs that there is a new atomic-clock technology based on a faster (THz) transition in a different atom, which may eventually supplant the cesium standard, but I can't find anything online with a brief search.
