When online auction giant eBay Inc (NASDAQ:EBAY) was founded in 1995, few people believed that the Internet would become the future of shopping. Few realized that the 28.8k text-based world known as the Internet would evolve into the broadband, wireless omnipresent cloud of today, seamlessly connecting our computers, smartphones and tablets.

Fast forward 18 years. Brick and mortar retail giants - such as Best Buy Co., Inc. (NYSE:BBY), J.C. Penney Company, Inc. (NYSE:JCP) and Sears Holdings Corporation (NASDAQ:SHLD) - now struggle to stay profitable. Consumers are increasingly using their smartphones and tablets to scan store items, turning their stores into giant, unprofitable showrooms.

Meanwhile, e-commerce giants eBay and Amazon.com, Inc. (NASDAQ:AMZN) are sitting pretty, enjoying comfortably brisk sales volume without being hampered by real estate and inventory issues.

Just as Amazon disrupted the tablet and e-book markets with its seminal Kindle Fire tablet, eBay is now looking forward into the future of mobile payments.

eBay is no longer content simply being an online auction site. It wants to replace your entire wallet or purse, as an all-in-one digital wallet, and that reality may be closer than you realize.

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A narrow earnings beat

eBay reported its fourth quarter earnings earlier this month, narrowly topping analyst estimates. The San Jose, California-based company reported adjusted earnings of 70 cents per share, or $571 million, on revenue of $4 billion. That represented a 62% decline in earnings per share and an 18% increase in revenue.

The dramatic year-on-year decline in earnings is nothing to be alarmed about, since earnings in the prior year quarter were highly inflated from the sale of Skype to Microsoft Corporation (NASDAQ:MSFT) for $8.5 billion in 2011. Adjusted earnings topped forecasts by a cent, while revenue was squarely in line with the consensus.

Historically, the stock has sold off after earnings (both positive and negative), but this time the stock rallied, for one major reason - PayPal.

The power of PayPal, Inc.

Without a doubt, PayPal - which eBay acquired a decade ago - has evolved into eBay’s most important asset. The digital payment system, which allows users to pay each other through e-mail addresses, is eBay’s preferred payment method, and is also increasingly accepted by other e-commerce retailers.

Just take a look at PayPal’s fourth quarter numbers:

Those five million new users represent the largest increase in PayPal users in eight years, as a testament to the increasing need for instant digital payments.

PayPal’s revenue is generated by service fees to merchants, similar to the ‘swipe fees’ of payment processors Visa Inc (NYSE:V) and Mastercard Inc (NYSE:MA) . PayPal’s mobile application has been downloaded onto over 120 million devices since its inception, and mobile payments accounted for 10% of PayPal’s total payments in 2012.

PayPal’s offline expansion

To expand its offline presence, PayPal users are given the option of signing up for a PayPal card, which works just like a normal debit card at participating stores.

eBay recently inked a deal with Discover Financial Services (NYSE:DFS), which will allow PayPal to be accepted anywhere Discover credit cards are accepted, starting this spring. This newly forged alliance could also help boost Discover's tiny market share (by purchases) of 3%, which is dwarfed by Visa's 57% and Mastercard's 25%.

In addition, eBay signed deals with 23 retailers, including Home Depot, RadioShack, Barnes & Noble and Abercrombie & Fitch, which will allow PayPal to be directly accepted as a form of payment.