Hi NoobKid!
Its not a stupid question, because one has to know the inner variables at play to understand how PoS works! The only thing is that whatever I am answering to you now is about to change...
At this moment, with the regular PoS in place, you do not have to keep your Vault application 1.3 open during the waiting period. Once you receive your coins at a given address, they start accumulating age - one day at a time, until 30 days pass. After 30 days, to receive your PoS interest then yes, you have to open the application and put it in staking mode (decrypted or decrypted for staking) and wait for your PoS reward to come in which may take some time (you don't receive it instantly).
Soon, with the upcoming PoSP, it will be necessary to keep the Vault 2.0 application running to earn your staking rewards; and you will see them coming to your Vault as you earn them (possibly you will get reward every day, or even multiple times per day if you have a big enough balance in your Vault).
Hope this helps!