In a LOFAR system, a "beamlet" is a pointing direction and a frequency channel (which is called a subband). In some ways, you can think of it as a "radio pixel" on the sky. These can be static, pointing at a fixed direction, or tracking, where they follow a particular astronomical object as it rises, travels across the sky, and then sets.
This rising and setting, and the motion of the stars generally, is dominated by the rotation of the Earth. Although some objects move about in the sky, due to orbits or proper motion, it is the 24-hour cycle of the Earth that is the dominant effect.
However, there are two points on the sky which do not move very quickly nor very much (although they do still move!). These are the Celestial Poles. These are the points at infinity that are projections of the Earth's rotation axis. Check the Wikipedia article for a full description.
So, in principle, if you were to point a beamlet at the North Celestial Pole (which is the one we see from KAIRA), then you would expect the power level measured to be absolutely flat. There is radio power coming from that direction, but it should remain constant, as it is only rotating within that radio pixel.
It is sort of flat... but not quite!
Here's an example:
The variations come from several things. Tall vertical spikes are radio-frequency interference. And the fuzzy-noisy patches can be from scintillating sources going through the side lobes.
More generally, gradual variations can be from larger areas of Galactic emission and discrete sources passing through the sidelobes of the beam pattern. And then there are subtle variations caused by snow on the antennas, temperature variations, receiver stability, etc.. These are much smaller, but are still present.
As a result, it can be quite a challenge to calibrate data from the instrument.
Such is the fun of radio astronomy! :-)