Word 2016 horizontal guide lines

I can think of two possibilities, neither of which is exactly what you describe.

1. There is the "grid," which provides horizontal and vertical lines at specified intervals. You display it by checking the box for Gridlines in the Show group on the View tab. Set the grid interval at Page Layout | Arrange | Align | Grid Settings. It's also possible that Use Alignment Guides on that menu is what you're looking for.
2. Possibly you had text boundaries displayed (File | Options | Advanced: Show document content), but you'd have a horizontal line for each line of text only if each line was a separate paragraph.

This is written relative to Word 2013, as I don't have Word 2016 installed. There may be some new feature in Word 2016 that I have missed.

Neither gridlines nor text boundaries...

In Word 2016 (and 2013 where the feature was introduced), there are alignment guides for positioning non-inline graphics.

Go to the Layout tab, or select a picture, text box, or other floating object so the Picture Tools or Drawing Tools ribbon tab appears. On any one of those tabs, in the Arrange group, click the Align button and click to put a check next to Use Alignment Guides.

What I have noticed in Word 2016 is that the guides don't appear if you insert a picture in a new blank document. As soon as you enter some text (just a paragraph mark is enough) the guides start working. This is different from Word 2013.

Are you referring to the document grid? In that case, you can switch it on by selecting the "Gridlines" option on the View tab (you'll find the option in the "Show" group).

Rereading the original post, I think it might be the gridlines after all. The spacing would have to be adjusted for the font size, though, to make them "one line apart".

I did test the alignment guides (which I already had enabled) in Word 2013, but they also didn't seem to match the OP's description (though I included them by reference, anyway).