Each brand has an identity translated through colors, shapes, core values, marketing... It needs to be clearly identified before creating a new product. This is especially important if you work on a freelance project, where you don't know the brand well.
Usually, already settled brands have a document, guidelines reporting all the things that make a product theirs. A new company or a new line of products might need to create its own DNA.
If you have to investigate by yourself to define the brand DNA, you should try to figure out how the identity of the brand is translated into colors, shapes but also the core values, what makes the brand unique, how people see it and what makes it different from competitors.
You can also hear "brand identity" which often refers to the visible elements like logo, colors that help the customer identify the brand. This aspect is particularly important in graphic design and UI.