I've often thought about this, because when I try and explain the game to my friends I invariably do a terrible job.
When asked the specific question, 'well, what did you do when you logged in last night?', responding with 'I orbited a gas cloud for 4 hours' or 'Spent my night building a spreadsheet for a manufacturing project', is often met with a little bit of laughter and mockery.
But to echo one of the points MacGybo mentioned. For me my enjoyment and love of the game stems from the social experiences. I love the community that has built up around EVE Online. I'm constantly interacting with the firneds I've made, but beyond that, engaging with new players in a support capacity, responding to some light-hearted shittalking with a fleet we've just had a scrap with or even seeing some of the quite intense role-playing aspects that a lot of people bring to the game.
Just last night I was with a small fleet of 8 pilots from my corporation heading around WH space looking for some PVP content. We took a fight with a smaller group thinking we had lured them into an unfair battle, only to find they absolutely wiped us! I and my corp mates lost a fairly considerable amount of in-game cash and were stunned at how easily we'd been dismantled, but after a few minutes of crying to each other and feeling sorry for ourselves, we've immediately jumped into trying to recreate the fits of our opponents and theorycraft other fleet compositions that would combat theirs. I've been receiving messages all day today with updates of what their fits might have been, it's been really quite distracting from work! :D
Basically.... it's great! But is so challenging to put into words what we're experiencing when we logged in. Thanks for asking the question because despite playing for nearly 10 years, I'm really curious to see what others answer with!