What is the practical link between the hashing power in the bitcoin network and its security? Several books claim that as the hashing/computing power increases, the bitcoin network is securer. How can a non-techie sees that from a practical standpoint?
Several books claim that as the hashing/computing power increases, the bitcoin network is securer. How can a non-techie sees that from a practical standpoint?

Bitcoin has the world's largest/most-energy efficient hashing infrastructure when considered as a whole.
Otherwise, someone would fire up some new miners, make most of the new blocks, don't accept transactions, and then turn off the hashrate to cause transactions to be unconfirmed for long.
But if your hashrate is high, this won't happen.
If the whole miner network were consisting of two computers and some smartphones, NSA or Google would be able to do what I just described above with their computing power.