It is one of the vaguest phrases in online dating. For one person, “fun” means a relaxed drink in Warwick or a gig in Leamington. For someone else, it means casual intimacy without plans for a conventional relationship. It can also describe discreet dating within an agreed open marriage.
Do not treat the phrase as automatic consent to anything. A profile is an introduction, not a contract. Ask politely and without turning the first message into an interrogation: “When you say fun, what sort of connection are you hoping to find?” That gives the other person room to answer in her own words.
If she is married, there is one more question worth asking early: does her spouse know she is dating? Some people practise ethical non-monogamy and have clear agreements at home. Others are having an affair. Those situations may look similar on a profile, but they carry very different emotional and practical risks.
Clarity is not unromantic. It prevents two people from arranging the same date with completely different expectations.
Be equally direct about yourself. Say whether you want conversation, occasional dates, a casual physical relationship or something that might become more serious. If exclusivity matters to you, say so. If you would not be comfortable dating someone whose spouse is unaware, that is a reasonable boundary, not a judgement you need to debate.