The short answer
Brand safety refers to the practices a business uses to avoid its content, ads, or partnerships being associated with contexts that could damage its reputation: controversial, offensive, or otherwise off-brand material appearing alongside a brand's name or advertising.
Where it shows up in an organic social context
Beyond paid advertising, brand safety is a real consideration when choosing influencer partnerships and content collaborations. A creator's past content and current behavior reflect on any brand associated with them, which is why vetting a potential partner's history matters as much as their current audience size.
A practical way to think about it
Before a partnership or placement, review a creator's recent history and the platform context, not only their current numbers. Brand safety issues tend to surface after the fact, when a review upfront could have caught the concern before any association was made public.