Can I deactivate health app?

Go to Settings > Privacy > Health and turn all apps off

Then there is no Health app usage. As any native iOS app, you cannot delete it (like the App Store, Clock or Mail or Safari app, among others).

To make sure there is no background usage, turn off Background App Refresh: Understand multitasking and background activity on your iPhone, iPad, or iPod touch - Apple Support

However, the Health app uses the motion processor in the iPhone hardware to count steps, like the compass or GPS do (GPS, not Location), so you cannot disable it.

You're welcome! That what it has to have a iDevice with a M7 motion coprocessor!

nitewish wrote:

Or is there a way to show e.g. the steps & distance from a day before today? I get these two statistics, but I found no way to select data from a special day. So I'd like to forget this app but I don't want it to work in the background.

There are lots of apps that will access the M7 co-processor data, just like the health app and will let you view the data in better ways. One of my favorites is the UP app by Jawbone. Just make sure you get the one that doesn't require the UP band. Moves is also very nice but not free. Also, not exactly what you're asking for but still worth a look is lark. If you search the app store, you'll find probably a couple hundred, some free, some at cost.

I think it helps to think of the Health app as a syncing conduit rather than an app you want to spend much time looking at. I use it to sync data between a number of different apps that otherwise wouldn't be able to share Health data.