In a community of mathematicians, an open problem is a question that no one has found the answer to. Open problems are not a source of frustration, they are a source of delight.
Open problems are the lifeblood of mathematics.
For you, as an individual mathematician, your own open problems are the questions you raise that you cannot answer. Anyone who does mathematics for very long soon discovers that open problems are abundant, and even more of them are generated as mathematicians think about something and ask themselves questions in an effort to understand it. One of a mathematician's hardest choices is deciding which open problems to give focused attention to and try to solve. When you raise a question for yoursef, and you cannot answer it, it becomes an open problem for you. Don't abandon your open problems just because they remain unsolved for a long time.