(1) Their store brands are consistently on-par or better than the name brands. It's no "Kirkland Signature" but I've found short of about three things, I like the Aldi product better[0].
(2) Their prices are good enough that I don't have to plan with coupons/nonsense. I analyzed this a few years ago (so long ago that newspaper coupons were still the only "real" coupons offered by food vendors) and found it was worth the time savings to skip the chore and just go to Aldi.
(3) Their "Aisle of Shame" (close-out random goods) is fun. I frequently find excellent products at ridiculous prices ($30 off-brand blender worked longer than the $200 I replaced it with).
(4) Their near-frustration free check-out.
Honestly #4 is the reason. Their check-out staff will rip through a cart faster than you can unload the groceries. They can do this because Aldi ensures their store branded products have barcode labels that extend the length of the box and appear on nearly every surface[1] (and they minimize the movements required of their staff to perform that job). You can have 4 people with full carts in front of you and they're cleared out before a typical Walmart scanner handles one half-full cart.
When I saw they introduced self-checkout, my heart sunk, but I used it. I think it's the only automated check-out system I've used that works. You get that product anywhere near the laser and it scans. It's amazing how much of that process comes down to the barcode scanner working properly.
[0] In one case -- their Mocha iced coffee -- I can't drink other brands any longer
[1] In some cases they slap a barcode on non-store branded products.