Inside each <a> element there's a hidden (using transform and opacity) <span> containing the text. Like this:

a span { 
 position: absolute;
 left: calc(100% + 1.5rem); //Moves it all the way to the right
 
 opacity: 0;
 transform: scale(0);
 transform-origin: center left;
 transition: .15s ease;
}

On hover or focus this span becomes visible through a transition of both transform and opacity. Like this:

a:hover span, a:focus span { 
 opacity: 1;
 transform: scale(1);
}

The <span> also has a psuedo-element in the shape of a rectangle, but rotated 45 degrees to make it look like a triangle. See the code for more details.