Closest
Search in your ancestors by items that match the selector passed, as specified. That is, searches in items that are up.
Consider the following structure:
<table>
  <tr>
    <td><a href="#">Link 1</a></td>
    <td><a href="#">Link 2</a></td>
  </tr>
  <tr>
    <td><a href="#">Link 3</a></td>
    <td><a href="#">Link 4</a></td>
  </tr>
</table>
Now imagine you intend that every time you click one <a>, that the color of <tr> in which it is inserted changes. In this case closest("tr") gives exactly the <tr> closer up in the DOM:
$("a").on("click", function(){
  $(this).closest("tr").toggleClass("cor");
});
.cor {
  background-color:cyan;
}
td {
  padding:10px;
}
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<table>
  <tr>
    <td><a href="#">Link 1</a></td>
    <td><a href="#">Link 2</a></td>
  </tr>
  <tr>
    <td><a href="#">Link 3</a></td>
    <td><a href="#">Link 4</a></td>
  </tr>
</table>
 
 
Note that if you change this closest for find will not work because the find just search in the children of the element where the search begins. Soon doing $(this).find in the <a> will search in the descending/child elements of <a> where there will be no <tr>.
See how doesn’t work:
$("a").on("click", function(){
  $(this).find("tr").toggleClass("cor");
});
.cor {
  background-color:cyan;
}
td {
  padding:10px;
}
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<table>
  <tr>
    <td><a href="#">Link 1</a></td>
    <td><a href="#">Link 2</a></td>
  </tr>
  <tr>
    <td><a href="#">Link 3</a></td>
    <td><a href="#">Link 4</a></td>
  </tr>
</table>
 
 
Documentation for the closest
Find
This method is used when you need to find elements descendants/children, match the specified selector. 
Taking also the previous structure we can change the goal so that each time the user click a line(<tr>) all of its <a> change colors.
$("tr").on("click", function(){
  $(this).find("a").toggleClass("cor");
});
.cor {
  background-color:cyan;
}
td {
  padding:10px;
}
tr {
  background-color:gray;
}
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<table>
  <tr>
    <td><a href="#">Link 1</a></td>
    <td><a href="#">Link 2</a></td>
  </tr>
  <tr>
    <td><a href="#">Link 3</a></td>
    <td><a href="#">Link 4</a></td>
  </tr>
</table>
 
 
I slightly changed the style to make it clear that you only need to click on the gray area, which is the area covered by <tr>. 
In this case also can not change find for closest otherwise the code will try to find a <a> above the <tr> that there is no.
Same example with closest to see that doesn’t work:
$("tr").on("click", function(){
  $(this).closest("a").toggleClass("cor");
});
.cor {
  background-color:cyan;
}
td {
  padding:10px;
}
tr {
  background-color:gray;
}
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<table>
  <tr>
    <td><a href="#">Link 1</a></td>
    <td><a href="#">Link 2</a></td>
  </tr>
  <tr>
    <td><a href="#">Link 3</a></td>
    <td><a href="#">Link 4</a></td>
  </tr>
</table>
 
 
Documentation for the find
							
							
						 
The difference is in the last word of what you understood of each :D A search in the element itself or up, another in the element itself or down, so to speak.
– Woss