"A conjecture [in mathematics] is an unproven hypothesis which appears correct." (Wikipedia)
If you notice a pattern forming when you're doing something with numbers, you might form a conjecture based on that. You haven't proven your statement yet, but you've made the connection between different cases, and can see a general formula emerging. Once you've done this, you can do more research and try to prove or disprove your conjecture. This is most of what formal mathematics is today.
