All of the coins vary significantly in price at different venues.

Keep in mind that Coinbase isn't a real exchange. They buy coins (probably from Bitstamp) and sell them with a smallish markup. So if Ethereum is cheaper on Bitstamp than Bittrex, that is the price difference.

Coinbase surely does some trade internalizing also: someone sells 10 ETH on the platform and you want to buy 5. They then match you with the 5 and match other people with the remaining 5. Of course, they will make their money on the spread.

Why are there such big differences in the prices of coins amongst the different exchanges? It is a funding problem. It is somewhat difficult to get fiat into crypto in most countries. If it was easy and also moving funds to different venues was instantaneous, then there wouldn't be any significant price differences. Algos would instantly arb out the price differences.