What is exactly the function of the LayoutInflater?
When you design using XML, all your UI elements are just tags and parameters. Before you can use these UI elements, (eg a TextView or LinearLayout), you need to create the actual objects corresponding to these xml elements. That is what the inflater is for. The inflater, uses these tags and their corresponding parameters to create the actual objects and set all the parameters. After this you can get a reference to the UI element using findViewById().
Why do all the articles that I've read check if convertview is null or not first? What does it mean when it is null and what does it mean when it isn't?
This is an interesting one. You see, getView() is called everytime an item in the list is drawn. Now, before the item can be drawn, it has to be created. Now convertView basically is the last used view to draw an item. In getView() you inflate the xml first and then use findByViewID() to get the various UI elements of the listitem. When we check for (convertView == null) what we do is check that if a view is null(for the first item) then create it, else, if it already exists, reuse it, no need to go through the inflate process again. Makes it a lot more efficient.
You must also have come across a concept of ViewHolder in getView(). This makes the list more efficient. What we do is create a viewholder and store the reference to all the UI elements that we got after inflating. This way, we can avoid calling the numerous findByViewId() and save on a lot of time. This ViewHolder is created in the (convertView == null) condition and is stored in the convertView using setTag(). In the else loop we just obtain it back using getView() and reuse it.
What is the parent parameter that this method accepts?
The parent is a ViewGroup to which your view created by getView() is finally attached. Now in your case this would be the ListView.
Hope this helps :)