The :only-child Selector is used to select the elements, who are the only child of their parent.
Let us simplify with the below example.
<html>
<head>
<title> My First Programme </title>
</head>
<body>
<h1> JQuery </h1>
<div class = "newClass1">
<p class = "para1"> First Paragraph </p>
<p class = "para2"> Second Paragraph </p>
<p class = "para3"> Third Paragraph </p>
</div>
<div class = "newClass2">
<p class = "newPara"> Next Paragraph </p>
</div>
<button> Click me </button>
<script src = "https://ajax.googleapis.com/ajax/libs/jquery/3.7.1/jquery.min.js"> </script>
<script>
$('button').click( function() {
$('p:only-child').text("The content of the only child got changed")
});
</script>
</body>
</html>
So, if you see the above code. We can see that there are three <p> elements, those are inside a <div> element.
<div class = "newClass1"> <p class = "para1"> First Paragraph </p> <p class = "para2"> Second Paragraph </p> <p class = "para3"> Third Paragraph </p> </div>
The corresponding DOM for it is,

Also there is another <div> element that has one child,
<div class = "newClass2"> <p class = "newPara"> Next Paragraph </p> </div>
The DOM for it is,

The <div> element has three children of type <p>.
<p class = "para1"> First Paragraph </p> <p class = "para2"> Second Paragraph </p> <p class = "para3"> Third Paragraph </p>
And the third child of <div> element is,
<p class = "newPara"> Next Paragraph </p>
And on button click, the contents of the <div> element with only child,
<div class = "newClass2"> <p class = "newPara"> Next Paragraph </p> </div>
Gets changed to The content of the only child got changed.
And this happened with the :only-child element selector.
$('button').click( function() {
$('p:only-child').text("The content of the only child got changed")
});The moment the button is clicked, JQuery statement gets triggered.
$('p:only-child').text("The content of the only child got changed")And the JQuery code locates the <p> element that is the only and changes its contents.