When combined, 兴趣 (xìngqù) becomes the noun for “interest.” Adding 感 (gǎn) turns it into a verb phrase: 感 (gǎn) + 兴趣 (xìngqù) literally means “to feel interest,” which is a very logical way to construct the idea of “being interested.”
While “to be interested in” is a universal concept, the Chinese expression 感兴趣 (gǎn xìngqù) is frequently used as a social tool for building connections (关系, guānxi). Asking someone “你对什么感兴趣?” (Nǐ duì shénme gǎn xìngqù? - What are you interested in?) is a very common and polite way to start a conversation and show that you want to know them better. In contrast to the sometimes more direct Western approach of stating opinions, expressing interest is a softer, more inviting way to engage. In a business context, saying “我们对您的方案很感兴趣” (Wǒmen duì nín de fāng'àn hěn gǎn xìngqù - We are very interested in your proposal) is a standard, positive, and encouraging phrase that opens the door for further discussion without making a firm commitment. It's a way of showing engagement and respect for the other person's work or ideas.
感兴趣 is a versatile and common phrase used in almost all aspects of daily life.