There are several things that DigitalOcean does differently. None of them stand out too much on their own, but together the combination does stand out. First is hourly billing. Spin up an instance real quick for testing, spin it down two hours later, one cent. If you do keep it up for a whole month, the charge is automatically adjusted to $5, so it's not like you really "choose" what billing period you want.
Second thing is simplicity. You may have seen DO's ads on YouTube - they poke fun at companies that have too many choices. Amazon EC2 comes to mind (though obviously they don't call them out by name). Instead of generating keys, selecting a type of instance, checking in to IP and bandwidth pricing charts, you have a simple structure. $5/month for a 512MB VPS, $10 for 1GB and so on, with other resources being adjusted as necessary.
A few other things that they offer are nice coupons to (new) customers, pure SSD storage by default, free snapshots and inexpensive backups, and fast support. All together, it's a winning combination for me.
Some weaknesses of their setup include lack of IPv6 (though a tunnel from HE.net adds very little latency), and only one IPv4 address per server. This is doubtless in an effort to maintain simplicity, which is understandable. If you need those things, DigitalOcean is not for you.