Updating the icon of every JLabel in a JLabel ArrayList
We will start by cleaning up the code:

First, let's make the for loop cleaner to read. A compiler is able to inline variables that are only used once in a scope.

for (int i = 0; i &lt; board.size(); i++) {

    final ImageIcon tileToDisplay = displayTile(i); 

    final int height = tiles.get(i).getHeight();
    final ImageIcon resizedTileToDisplay = resizeIcon(tileToDisplay,height,height);
}


Second, in displayTile(int num), StringBuilder is more efficient when concatenating strings. Also, if(num != 0) is redundant because you apply the same logic in both cases.

public static ImageIcon displayTile(int num) {

    final StringBuilder pathBuilder = new StringBuilder("src/resources/");
    pathBuilder.append(num);
    pathBuilder.append(".png");

    return new ImageIcon(pathBuilder.toString());
}


Lastly, resizeIcon changes the parameter i; methods should not change the parameters that they receive:

public static ImageIcon resizeIcon(ImageIcon icon, int x, int y) {

    Image resizedImage = icon.getImage().getScaledInstance(x,y,java.awt.Image.SCALE_SMOOTH));
    return new ImageIcon(resizedImage);
}


Now, let's deal with performance:

You are loading 100 - 200 images from a file, resizing each one and then placing it on a screen. This is a resource intensive task and you need to optimise it. Here are some suggestions


Use a ThreadPool to load the images asynchronously on start up. Cache them in memory and use them as needed.
Only load images as needed. For example, the board may have 200 tiles, but only 10 are visible at a given time. So load the first ten tiles. Anticipate which tiles will be needed and load them as necessary
If resizing is a one time operation, perhaps saved the resized images to disk so that you won't have to resize them after the first time.
BufferedImage offers getSubimage. You could have one big image with all 100-200 tiles. Load this one big image once, and then show only the relevant part of the image using getSubimage. This is a concept known as Sprites and you can find a clearer example here.