What do these parts of this PCB do?
That’s a microstrip radial stub these are used for impedance matching when a low-impedance stub is needed. Their shape allows for a narrow connection point to the main microstrip. 

When used in pairs these are also known as butterfly stubs, or bowtie stubs. 

As any other stub, these are used to match the input/output impedance of a circuit element to another, to maximize power transfer and minimize reflections. These also “tune” a microstrip, as their impedance-matching characteristics is wavelength-dependent.