Beam broadening is the gradual widening of a radar beam's cross section as it travels away from the antenna, so the sample volume at long range covers a much larger patch of atmosphere than it does close in. The same physical storm looks sharper near the radar and blurrier at distance, without anything about the storm itself changing.
Why the beam spreads
The main lobe of a radar antenna is not a laser. It leaves the dish as a narrow cone, and geometry does the rest. A WSR-88D antenna emits a beam with a nominal beamwidth near one degree, and that angular width becomes a physical width that grows linearly with range.
At 60 nautical miles the beam is already over a mile across. At 120 nautical miles the same beam is more than two miles wide and several thousand feet tall. Every pixel on the display averages reflectivity and velocity across that whole volume.
How forecasters read a broadened beam
Distant storms look grainy and blocky because each range gate is drawn as a large sector. Fine features that would be obvious near the radar, such as a tight rotation core, a hook, or a narrow updraft column, get smeared into their surroundings.
Forecasters compensate by pulling a nearer radar into the picture when one is available, and by remembering that a small feature at long range may not be resolvable at all. Two circulations that appear as one blob at 100 nautical miles may split into a pair when a closer radar reaches the same storm.
Where it misleads
A storm sampled by a wide, high beam can look weaker in reflectivity than it actually is, because heavy cores only partially fill the volume being averaged. The same effect can hide low-level rotation entirely if the beam is above the layer where the circulation lives.
Beam broadening also inflates apparent storm size, since a small cell drawn inside a wide gate paints as a bigger patch than it is. Treat detail from any distant radar as a floor on what is happening, not a ceiling, and lean on closer radars, dual-pol signatures, and surface reports before drawing conclusions.