The phrase implies a slow, not immediate, effect on something that grows over time. The consistent late payments began to nibble away at the company's capital.
Pro Tip 2/3
Negative Sense
Often used to describe something losing value or quality, generally with a negative outcome. The new policy is nibbling away at employees' trust in management.
Pro Tip 3/3
Metaphorical Use
Can be used metaphorically to describe non-physical entities, such as time or abstract concepts. Procrastination nibbles away at my productivity.