For what seems like years Google has been rumored to introduce a Paypal killer. Google Checkout could be it. Google Checkout, according to Garret Rogers, may be a simple solution for purchasing stuff online; something that could be integrated into Google Analytics as well as allow businesses to track purchases via easy-to-use web stats.
This is all rumors and speculation at this point but it does seem like the name implies some type of business-oriented product. However, if this is the concept behind Google Checkout than this only half competes with Paypal. Paypal is mostly used for purchasing through its parent-company eBay but it is also used to send money across the web. Based on these rumors, Checkout does not seem to compete with this area of Paypal's market.
For quite some time (possibly 2 or more years; I can't remember), it has been rumored that Google would come out with a Paypal-killer called Google Wallet that would be almost the same as Paypal. I don't know whether the Google Wallet concept still exists or if Google Checkout is the replacement (can there be a replacement for something that has never existed?) for Google Wallet; or possibly that Google Checkout and Google Wallet will someday coexist in the same online-money world.
Right now both Google Wallet and Google Checkout is all rumors and speculation so take this with a grain of salt.