What do I do after I merge feature files with a remote server? I'm having real trouble getting my head around the Features module. Would someone be able to help me understand it a little better? Perhaps describe it in laymans terms?

Here's the scenario I am working on right now:

I've made a change to some mini-panel and want to move those changes to a remote server with Features.

I create that feature and add the mini-panel and download the files. This part seems fine - I can even view my changes in the file's code. I then merge these files onto my remote server.

It's here I get a bit stuck. Now what do I do?

When I find my Feature in /admin/structure/features it's overridden. What do I do next to update my mini-panel on the remote server?
You will have to revert the feature, So that the configurations in the remote server would be same as that in the code. Feature overridden means, the config in the Code and that in the server is not the same. So by reverting the feature you make the code and the db config the same. Please be cautious while reverting the feature, Sometimes the changes which you have done directly in the server would be lost. It'd be best if you test reverting the feature in your staging environment first.