The equation represents the Direct Form I IIR Filter equation. Each band of the EQ implements the transfer equation given in this page.
The Biquad filter on the record path only has one EQ band, and the parametric EQ on the playback path can be programmed to be a 3, 5, or 7-Band EQ.
Each band of the EQ implements the transfer equation given in this page.
The coefficients are normalized such that a0 = 1
From basic DSP theory you can see that the equation is an IIR filter transfer function of in the Z-domain. The biquad filter, as shown in the equation, is a 2-poles 2-zeroes equation. From this information one can visualize that depending on the location of the poles and zeroes the frequency response changes.
Here are a few links to online tools and articles that go more in depth on how this equation can be related to Frequency, Gain and Q.
Digital biquad filter - Wikipedia Article
Filter design tool - Online
And this final article does a good job of breaking down some of the equations for each filter as used on the EVkit GUI.
Cookbook formulae for audio EQ biquad filter coefficients
Keep in mind in the implementation code you need to normalize all the coefficients to coefficient a0. Then you need to multiply the results by 2^20, and round the results. These final values are what go into the registers for the coefficients as specified in the data sheet for each of these products.