What exactly is a nucleation core?

There is no such thing as a nucleation core, however there is such a thing as a warp core.  Most starship engines have them...they allow the spaceship to travel faster than the speed of light.

a nucleation core (aka nucleation site) is simply a location where a rapid, repeatitive, cascading reaction can be initially triggered.

[ this is easier understood using examples. So, i have provided three below, each separated by a '----' line.  
In retrospect, I realize i kinda wrote a lot, so if you get the first example, don't feel like you need to read the others.
At the end, after a "====" line, I explain nucleation in context of Arp 2/3]

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EXAMPLE #1

take, for example, a soft drink.  

the soft drink has lots of carbon dioxide dissolved in it; but that carbon dioxide would "like" to escape into the atmosphere (and by 'it would like to' i really mean that this process increases the entropy of the system and therefore is favorable.)

however, this process takes a lot of "effort".  Individual molecules must undergo a phase change, forming a gas, and then join together and overcome the pressures of the surrounding fluid so that a tiny bubble can form.  Then once the bubble is formed it is much easier for more gas molecules to join the existing bubble.  

this is because a nucleation site has been formed.  Once the bubble is started (even if microscopic) it is much easier for subsequent molecules to join existing bubble by undergoing a phase change, than it was for the initial CO2 molecule to
under go a phase change.

(of course, eventually the bubble gets big enough to provide enough buoyant force to rise to the top of the glass and out of the coke.)

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EXAMPLE #2

Another example is ice forming in water.  If you cool water VERY slowly and in a VERY still environment (ie you don't bump the container, etc), it is actually possible to get liquid water to drop slightly below 0 degrees C without freezing.  This is because there is no nucleation core for the process to begin.  

if you were to take this 'super cooled water' and touch it with a tooth pick or a piece of ice or something, the whole thing will nearly instantaneously all freeze in a cascade motion starting at the touching object.


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EXAMPLE #3

similarly if you ever made rock candy as a child in a science class, you took a super saturated sugar/water solution and dipped a stick or a piece of string into the water and then after a while candy "grows" on the stick/string.  theoretically, the candy could have formed anywhere in the solution; however, the string acts as a nucleation core.



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Actin filaments are made thousands of actin molecules joined together:
http://academic.brooklyn.cuny.edu/biology/bio4fv/page/actin1063.JPG

the Arp2/3 complex provide a site that initiates the joining of a few actin particles.  Once this has been been initiated, the actin strand elongates by the addition of many more particles subunits (called "polymerization").  

Once the reaction has been started, polymerization requires very little assistance.  However, it needs a nucleation site to get started:  enter Arp2/3.

in this way Arp2/3 complex can guide the structural development of actin strands and their branching properties, etc.

hope this helps!