The Universe is filled with background radiation left over from shortly after the big bang. Once very hot, the expansion of the Universe has lowered the energy of this radiation down to that of a black body at a few degrees Kelvin. This is known as the Cosmic Microwave Background (CMB). This radiation is remarkably uniform, because the Universe was itself very uniform at the time this radiation was released. However, it is only uniform when properly measured. When we measure CMB radiation, we find that the energy is higher in one direction and lower in another. This is because our instruments are moving. The Earth is moving around the Sun, which moves within the Milky Way. The Milky Way is moving with respect to our local cluster of galaxies, and we can suppose it continues all the way up from there. When moving at these high speeds of hundreds of kilometres per second, our view of the CMB radiation is distorted. We see it as having higher energy in the direction of motion, and lower energy in the opposite direction, through a process analogous to the Doppler effect.
This creates a dipole along the direction of motion, which we call the kinematic dipole. We subtract this before looking at the CMB. But how do we know what the dipole is? While we can measure a few of the contributing speeds easily, such as the Earth around the Sun, we don't know the total sum for our net speed relative to the Universe as a whole (the definition of which is also of concern).
We simply assume that the entire dipole is kinematic, and go backwards from there to find our velocity.
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