Will this app https://itunes.apple.com/in/app/repost-for-instagram/id570315854?mt=8 come under the category of displaying & accessing third party content?
Yes, it uses the Instagram logo which is 'third party content'. When submitting an app like this, you will get another question asking if you have permission to use it. For uses like this, it generally means that you need to display the logo in a 'proper' way; what 'proper' means varies from company to company, but it usually includes things like not changing the color of the logo.
For the content, again this will vary per company, but usually you have to sign an agreement when using the SDK of said company. I don't know the specifics for Instagram, but this could include a section about giving you permission to show the content in your app, provided that you give attribution (to the company, the author of the photo, or both).
From the documentation:
It’s your responsibility to determine and follow regulations that apply in each territory.
This is probably so that such third parties cannot sue Apple because there is an app available in their App Store violating the regulations; Apple will forward such complaints directly to the developer of the app.