Let me send along the following, layperson explanations of the two experiments.
ARA and IceCube are both looking for neutrinos from high-energy systems in the universe. Neutrinos are small, nearly massless subatomic particles that pass through material with only the rarest interactions. In fact, IceCube is most interested in neutrinos which have already gone through most of the Earth and happen to interact in the ice near the detector going upwards. IceCube looks for the light emission from the neutrino interactions in the ice. ARA looks for a coherent pulse (lasting on order of a billionth of a second, a nanosecond) of radio emission. We use the ice because it is both light transparent and radio transparent. The remoteness of the site, the South Pole, reduces the anthropogenic backgrounds so the real physics signal stands out more clearly. In detail, the two experiments are optimized for different energy ranges: IceCube for lower energies, and signals associated with supernovae, and ARA for higher energies, and signals associated with the most energetic particles in the universe (the so-called GZK cosmic rays).
There is a lot more, at layperson, general scientifically trained audience, and technical levels on the IceCube website. There are a couple of less technical explanations of the ANITA experiment which is a balloon-borne experiment which is the intellectual godmother of ARA: for example, http://www.phys.hawaii.edu/~anita/web/science.html.