Shorthand for "electronic meet." Used when two parties meet or are introduced to each other for the first time via an electronic medium such as email, IM, Twitter, facebook, etc...
After a he had been contacted by email from a vendor he had never met before, Josey wrote back: "It is a pleasure to e-meet you and I look forward to servicing your needs with my quality computer consulting."
Modern day replacement for 'pleasure to make your acquaintance', often used by pretentious (and often vapid) individuals with no imagination or sense of how ridiculous they sound; typically found in the world of online marketing.