Likely you were able to set up your harmony hub as a thing, but you were not able to set up having SmartThings activate harmony activities, because that’s the part that’s broken right now. (update: there’s a workaround that avoids the crash–details in the Harmony FAQ linked to below.)
When it’s working, you can basically have anything you can do in smartthings activate a harmony activity. Flip a switch, trigger a motion sensor, change the mode, change alarm status, run a time schedule, detect someone coming home, etc.
So what you can do in harmony is anything you can do in harmony, which is a lot. Controlled by any rules you can set up in SmartThings. So very cool. 
Harmony “Activities”
You do have a button remote with harmony and if you are physically able to use that, then that works great.
But the real power is in harmony’s concept of “activities.” These don’t even have to be associated with a specific button on the physical remote. They are basically like a “macro” or a “script” that let you pretty easily combine instructions for multiple devices. Some devices controlled by harmony, some devices controlled by SmartThings.
Then you can start that activity in many different ways. People who only have harmony can use a harmony phone or tablet app to start an activity. Or of course the Harmony remote. But you can also have it start because you do something with a different device, or even a time of day schedule.
The usual example is having a motion sensor trigger a “movie night” activity which turns the lights down, Closes the curtains, and turns the TV on.
Add Alexa into the mix and it could be a voice command: "Alexa, trigger movie night. "
You might also have an air conditioner which can be controlled by harmony. Or a game box. Or a sound system.
So to figure out what you want to do with it, you start by looking at what harmony can do on its own with devices you are interested in. And then you add SmartThings as a scheduler. Or Alexa as voice control.
if the SmartThings integration is broken, what does work now?
The good news is that there is an official Alexa/harmony integration using the free IFTTT service which works just fine and doesn’t require SmartThings at all. So that gives you voice control of Harmony activities. 
See the first post in the following thread for how to set up the IFTTT method. It’s quite easy.
When you see people talking about “Alexa, trigger TV” they are talking about the IFTTT integration that doesn’t need SmartThings. If you see them talking about “Alexa turn on the TV” then they are using the SmartThings integration.
If, as is possible, the integration is not broken when you start from the harmony app, then you’ll also be able to add SmartThings devices into harmony activities, so you could still use sensors and have the lights go down from the harmony activity.
It’s possible that the only thing that is broken is using the SmartThings app to start harmony activities. or it’s possible that they fixed it today, I haven’t looked yet. Or it’s possible that it’s working for some people but not others. All of these have happened in the last week.
Here’s the FAQ that you use to set up the full two-way harmony/SmartThings integration once it is fixed:
Needed equipment
You need one harmony home hub within infrared range (I R) of the equipment that you want to control via IR with harmony. Because it’s also a universal remote, people typically get one remote for each TV. How many hubs you need depend on the layout of your home and whether you want to run wires to IR blasters in other rooms. That just depends on your specific layout.
You will not need the harmony hub extender if you are using SmartThings. The extender’s main purpose is to let those who only have harmony add motion sensors to their set up. But if you’re using SmartThings to control your motion sensors then you don’t need the extender. And a sensor can only report to one of these so if you do decide to add a sensor to the harmony extender you could no longer use it with SmartThings. But because the SmartThings hub and the harmony hub can talk to each other, you can have the sensor controlled by SmartThings and still use it to trigger A harmony activity.