From Unofficial BOINC Wiki
Einstein@Home searches through data from the LIGO gravitational wave detectors, looking for a signal from a "continuous wave" source, which would be the gravitational analog of a pulsar. In fact pulsars (ie. electromagnetic pulsars), which are thought to be spinning neutron stars, are a likely candidate for producing gravitational waves, so long as the neutron star is not symmetric (specifically, has a non-zero quadrupole moment).
While LIGO has previously conducted "directed" searches aimed at particular known pulsars, Einstein@Home is conducting an all-sky "blind" search, which means that it is searching every part of the sky and a wide range of signal parameters (primarily frequency and spin-down rate). This is a massive computational task which could not be accomplished with traditional computing resources.
Gravitational waves were predicted by Einstein in 1916, but they are expected to be very weak and have never been directly detected. LIGO seeks first to detect gravitational waves, and then to use them for astronomical observation.
Einstein@Home is currently searching the most sensitive 840 hours of data from LIGO's first science run at design sensitivity (S5R3).