The solar model tells the density, temperature, and pressure of the gas at every point in the sun. Given the mass, composition, and age of the sun, this model reproduces the observed luminosity and radius of the sun precisely. This success is reassuring, but we would like more convincing evidence that our theory is correct. The period of a typical oscillation is about 5 minutes. Solar astronomers can measure these oscillations very precisely using Doppler shifts.
Theorists can predict the oscillation behavior from the solar model.
The precision is high enough to allow tests of fine details of solar theory, like rotation of the solar interior, or the slow settling of heavier elements towards the center of the sun over its lifetime. The sun is opaque to photons, so we don't see into the center. Typically, a block of lead about 1 light-year long is needed to stop a neutrino. But neutrinos are hard to capture. With a big detector, one can expect to see a few dozen reactions per month caused by solar neutrinos.