Which words are you having trouble with? That's pretty straight forward, but I'm assuming you're wanting to know more about the across devices thing... This is actually one of my favorite features. Their system keeps track of where you're logged in from and whether you're active or idle on that platform, then if you are sent 1-1 messages or mentioned in a room it will find you, delivering to a computer client first, then push notifications, then email--which is really valuable for us.

>it makes team communication easy and painless on every device our employees own

Is this sentence really that hard to understand?

Team communication: Teams need to interact in a variety of different ways: public groups/private groups, fixed groups/ad-hoc groups, groups/1-2-1. HipChat supports a variety of different ways of interacting, and does so in a way that's easy to use. People nowadays use a variety of different devices (and classes of device). HipChat has a range of native clients, plus a web based one, and so can be used on most of the devices that people want to use it on. (We use Slack, but I've tried and liked HipChat too)