you for those answers. So then what does securing your wallet do for you? I mean how does that stop someone from using the part of the block chain assigned to you?
The wallet contains private keys that are mathematically associated with the bitcoin addresses that you control.
The only way to re-assign value that is associated with a bitcoin address to some other bitcoin address is to provide a valid digital signature created with the private key that is associated with the address that currently has the value associated with it.
Therefore, anyone who has access to the private keys in the wallet can spend/steal the bitcoins by creating the digital signature and re-associating the value with some new address.
Securing the wallet prevents others from obtaining the private keys that are stored in the wallet.
The blockchain is a public ledger containing every transaction that has ever occurred in bitcoin that every full peer maintains a full copy of. Every peer (and every miner/pool) will verify the digital signature on the transaction spending bitcoins before relaying the transaction to any other peers or updating their own copy of the blockchain with it.