I am also not too clear on the concept of Bitcoin core .like does it refer to something like a server that hosts the Bitcoin network or does it refer to the entire block chain system
Bitcoin core is a bitcoin wallet and also a tool for running a bitcoin node, downloading the blockchain and validation of transactions.
Note that you don't have to run your own node and use bitcoin core. There are many other wallets that you can use for receiving and sending bitcoin.
You can use bitcoin core if you want to running your own node.
With running your own node, you can have a copy of the blockchain and you don't rely on others servers when you want to broadcast a transaction or get data from the blockchain. In this way, you can protect your privacy and you also help the network to be more decentralized.