Hopefully an example that’s not too prickly: I’m from the south of the US. I don’t have a southern accent (except when drunk or sleepy!). A lot of people, myself included, have an unconscious bias that people with southern accents are less intelligent than people without. However, I’ve known lots of smart people with southern accents, and lots of unintelligent people without them. I don’t know why I have this bias: it was instilled in me by the culture I grew up in, I guess. But, because I am aware of it, I can watch out for those reflexive feelings that make it more likely for me to dismiss something someone is saying just because of their accent. I can adjust my actions to align with the kind of unbiased person I’d like to be, even though I can’t control the lingering feelings the bias creates.
This is the general idea of wanting people to be aware of their implicit biases: not to judge them due to those biases, but to help them see that, due to societal or cultural or familial influence, they may not be living up to the kind of person they’d like to be. There’s a huge difference between someone who’s consciously racist and someone who has racist priors due to the culture they grew up in. Many in the latter group accidentally propagate racist systems, even though they would never want to do so if they had a conscious choice. But it’s hard for anyone to see how their subconscious affects their day-to-day opinions. The hope of teaching about implicit bias is that people can see its effect in their lives and make adjustments, hopefully reducing the systemic problems that people face in the process.