How does a wifi antenna work?
I don't agree with the other answers that describe this as a monopole antenna. I believe it's actually a coaxial dipole antenna, first described in a 1939 Bell Labs patent.  Just for fun, I'm embedding one of the illustrations from that patent here.

How do I come to this conclusion? First, it's much longer than 1/4 wavelength at wi-fi frequencies (2.4 GHz = 12 cm wavelength). Second, the larger-diameter base section and thinner-diameter tip are unnecessary bulk for a simple monopole whip.
The advantage of the coaxial dipole is that it does not require a ground plane. The purpose of the thicker base section is to form a quarter-wave &quot;choke&quot; that isolates the lower tip of the dipole from the coaxial feedline.
This type of antenna is technically &quot;ground independent&quot; meaning a ground plane is not essential to its operation. The radiation pattern will still be affected by the router chassis in proximity, but not as strongly as if it were a quarter-wave monopole.