Take the noun, onus, as a formal word for responsibility or obligation. If your teacher assigns onus as a vocabulary word, it puts the onus on you to find out what it means.
Onus is a formal or sophisticated way to say "responsibility" or "duty." It sounds a little like the unrelated word owner, so think about the person with onus as owner of the responsibility. If the onus is on you to organize a fund raiser, you have to set the whole thing up. Have you ever heard the legal term onus probandi? It means the burden of proof, which requires the accuser to prove the case against the accused.