Do iPhones have a built-in mouse or trackpad and how do I use it? Quite some time ago someone told me (or maybe I read it) that iPhones have a built-in trackpad or mouse pointer that makes it easy for you to move the cursor around for editing text. I want to know if this is actually possible? 

Right now my computer is in for repairs and I’m stuck using an iPhone to edit a Word document and being able to do this would be great if its possible, but I can’t see any options anywhere in the settings.

So is it true that iPhones have a built-in trackpad or mouse pointer function? And how do I get to use it?
iOS 13 and later
As of iOS 13 and above the process for using this feature has changed.
The steps are largely the same as for iOS 12 and earlier (see below), but instead of pressing hard on any of the keys on your keyboard, you need to press on the space bar and not let go to see and use the trackpad.
The other change is that this feature is now available to any iPhone compatible with iOS 13 or later, not just iPhones with 3D Touch. So, models like the iPhone SE are now covered!
iOS 12 and earlier
Yes, this is true but not for all iPhones. It has to be an iPhone 6S or above (basically any iPhone with 3D Touch, which unfortunately means the current iPhone SE is not included).
The way to access it is via the keyboard, so you need to already have the keyboard visible on the screen.
More specifically, follow these steps:

Press hard on any of the keys on your keyboard (but don’t let go)
After a moment your keyboard will turn into a grey “trackpad”, so to speak (remember, don’t let go)
Now move your finger around the grey trackpad area (where your keyboard was) and this moves your cursor around the editing area (so if it’s only a small field, you can only move the cursor around that, if it’s your Word document, you should be able to move around the page).
As soon as you let go, the trackpad disappears and your keyboard returns, and you can start typing from where you left the cursor.

Highlighting text
Since you’re stuck having to edit a Word doc on your iPhone, you’ll probably need to know how to highlight text while using the above feature. This is a little tricky, but you just move the cursor to a word you want to highlight and then reduce the pressure on your finger ever so slightly for a moment and then press hard again. This should highlight the word for you.
Note:- This may take a little while to get used to and, while handy, certainly doesn’t make the job of editing a Word document on your iPhone easy! But it is handy for small notes or adding comments to news stories, etc.
[EDIT]
Below are two screenshots showing a before and after shot of how this works when using this mode to edit this very answer!