Measuring gravitational waves
The relative distance change between two freely falling bodies caused by a passing gravitational wave is exceedingly small, because spacetime is an extremely stiff elastic medium. For example: Gravitational waves of a typical white dwarf binary at a distance of 50pc create a periodic change of only 10-10 m in distance between two test masses, separated by a sufficiently large distance.
A suitable instrument for measuring such small length changes over a broad band of low frequencies is a laser interferometer with an arm length as large as possible and long integration times, the primary impetus for a space-borne detector.
Hence eLISA/NGO can be thought of basically as a Michelson interferometer in space with an arm length of 1 million km. The arm length has been carefully chosen to allow observation of most of the interesting sources of gravitational waves.