The term 女孩 (nǚhái) is a modern, neutral word that doesn't carry heavy historical baggage. However, its usage exists within a culture that has undergone significant shifts in gender roles. Historically, China was a society with a strong preference for sons (重男轻女, zhòng nán qīng nǚ), a concept that still has residual effects today. In a modern context, 女孩 (nǚhái) is used much like “girl” is in English, but with slight differences in nuance. In Western culture, calling an adult woman a “girl” can sometimes be seen as diminutive or patronizing. In China, while calling a middle-aged professional a 女孩 would be inappropriate, a boyfriend calling his 25-year-old girlfriend 我的女孩 (wǒ de nǚhái) (“my girl”) is considered sweet and affectionate. An older person might also refer to a young woman as a 女孩 in a friendly, avuncular way. The key is the relationship and power dynamic between the speakers. It's generally a term that implies youthfulness and a sense of endearment.
女孩 (nǚhái) is an extremely high-frequency word used in all sorts of daily situations.
The term is generally neutral to informal. In formal settings or when showing respect to an adult woman, you would use 女士 (nǚshì), which is equivalent to “Ms.” or “Madam.”