I can think of a couple of ways to do this. With TYPO3, there are so many different ways to accomplish anything.

For purposes of illustrating how to show content only on the front page, this example will use a typoscript object called lib.onlyonfrontpage.

In my template, I have created this object as follows:

lib.onlyonfrontpage = TEXT
lib.onlyonfrontpage.value = <h1>This will only show on the front page of the site</h1>

And the object can be called by placing the following typoscript below it in th template setup:

page.1 < lib.onlyfrontpage

So thus far, the typoscript I've added to my template looks like this:

lib.onlyonfrontpage = TEXT
lib.onlyonfrontpage.value = <h1>This will only show on the front page of the site</h1>
page.1 < lib.onlyonfrontpage

So once the above typoscript is in the root typoscript template of the site, every page will show text which says "This will only show on the front page of the site".

Method 1: Use "globalVar" along with typoscript conditions

Yep, one way to make the text only appear on the front page could be to use a condition based on "globalVar". This only involves two lines of code to be added to the above example.

lib.onlyonfrontpage = TEXT
lib.onlyonfrontpage.value = <h1>This will only show on the front page of the site</h1>
[globalVar = TSFE:id = 1]
page.1 < lib.onlyonfrontpage
[end]

Notice that TSFE:id is set to "1" in the above example. It is set to equal "1" in this example because on my site, the uid of the home page is "1". Put whatever the uid of your home page is there.

By modifying the value of TSFE:id in the above example, you can also show your content on any particular page (or pages) of your site.

For example, if I only wanted to show my content on the pages with page id's equal to 13, 7, or 3, then that can be done as well, and the typoscript which would do that would look like this:

lib.onlyonfrontpage = TEXT
lib.onlyonfrontpage.value = <h1>This will only show on the front page of the site</h1>
[globalVar = TSFE:id = 13,TSFE:id = 7,TSFE:id = 3]
page.1 < lib.onlyonfrontpage
[end]

Method 2: Use "treeLevel" along with typoscript conditions

Using the treeLevel feature of typoscript allows you to show your content only on the front page without having to know the page id of the homepage of your web site. This can be useful if you want to use the same template on multiple web sites which might have different home page id's.

The condition syntax is mostly the same as above. Here's the example which accomplishes the same as above but using treeLevel:

lib.onlyonfrontpage = TEXT
lib.onlyonfrontpage.value = <h1>This will only show on the front page of the site</h1>
[treeLevel = 0]
page.1 < lib.onlyonfrontpage
[end]

So, that's another way to do it.

Method 3: Using typoscript if statements

I like using if statements in typoscript for a lot of purposes. Here's how if statements could be used to show content only on the front page, assuming the page id of the front page is "1".

lib.onlyonfrontpage = TEXT
lib.onlyonfrontpage.value = <h1>This will only show on the front page of the site</h1>
page.1 < lib.onlyonfrontpage
page.1.if.value = 1
page.1.if.equals.data = TSFE:id

Other Possibilities

Above I've demonstrated a few different ways using typoscript to show a particular content item only on the home page of a TYPO3 web site. I'm sure the ways I have mentioned are not the only ways to do it. 

The thing I like most about TYPO3 is that there are a multitude of different ways to perform any given task. This is also the thing that made TYPO3 difficult to understand when I first began learning TYPO3.