And what to do next? I guess it should be linked somewhere.
The plugin loads your language itself, so you don't need to do anything. However, it must be named correctly.
I added my translated .po and .mo to language file.
Where and what are they named?
For Slovak your MO file must be named bookingup-sk_SK.mo
. *
As for location. You can put this file inside the plugin's language folder but be warned that plugin updates will remove it!
You can also place the file under wp-content/languages/plugins/
but this location is not entirely safe either. Make sure you back your files up after making any translations.
* Note that this plugin does not follow WordPress conventions, which is why it has no community translations. It should use the text domain "booking-ultra-pro" but instead uses "bookingup". That's fine as long as you know and as long as it loads itself, which it seems to do.
If you want any more help I'm going to need more details about what you've done and what isn't working. If you update your question, I'll update my answer.