If you're hopeful about something, you're optimistic. You think it's going to turn out OK. Your team has been doing well in practice, so you're hopeful that you'll win the finals.
Hopeful comes from the word hope, meaning "optimism about a future event," and the suffix -ful, meaning "full." So if you're hopeful, you're full of hope: you think something good is going to happen. You might be hopeful that you'll be offered a job after your great interview. Used as a noun, hopeful can describe a promising person who wants to succeed at a particular goal. The charismatic young politician is a hopeful for the next election.