Bitcoin-qt is a Bitcoin wallet. Your Bitcoin wallet is what allows you to transact with the world. It gives you ownership of Bitcoin addresses that you can use to receive coins from other users, and then lets you send those coins onwards. Just like email, you can receive Bitcoins when you are offline and all wallets are compatible with each other
Bitcoin is a decentralized P2P electronic cash system without a central server or trusted parties. Users hold the crypto keys to their own money and transact directly with each other, with the help of the network to check for double-spending.
As a new user, you only need to choose a wallet that you will install on your computer or on your mobile phone. Once you have your wallet installed, it will generate your first Bitcoin address and you can create more whenever you need one. You can disclose one of your Bitcoin addresses to your friends so that they can pay you or vice versa, you can pay your friends if they give you their addresses. In fact, this is pretty similar to how email works. So all that is left to do at this point is to get some bitcoins and to keep them safe.