Bokeh Vector Background in Illustrator
Create a new document of 600 x 600 px.
Let's create a base background for our image.
Grab the Rectangle Tool (M) and click on your canvas. Set the dimensions to 600x600 px, then hit OK. Open the Color window (F6) and set its Fill to 90% black. If you don't see the grayscale "slider", open the drop-down menu from the top right corner of the window and select "Grayscale". Make sure you have no Stroke on the rectangle.
Let's align our shape with the canvas.
Select the rectangle using the Selection Tool (V), then open the "Align to clipboard" menu on the top menu bar. Now click the "Horizontal Align Center" and "Vertical Align Center" buttons.
Open the Gradient window and add the colors like below. Then apply it to our shape at a -45 degrees angle.
Open the Transparency window (Window > Transparency or CTRL+SHIFT+F10) and set the rectangle's transparency to Overlay.
Grab the Ellipse Tool (L) and click your canvas. Set both Width and Height to 407 px. Now set the Fill and Stroke colors like below. Open the Stroke window (Window > Stroke and set Weight to 3 px.
Select the newly created circle and go to Effects > Blur > Gaussian blur and give it about 11 px. Then hit OK.
Place it over the square and set Transparency to Color Dodge and Opacity to 39% in the Transparency window (CTRL+SHIFT+F10). It should look like below.
Repeat Step 6: create a circle with the same colors, but this time set Weight to 2 px and make the circles smaller. Create a few of different sizes. Now select the newly created circles (use Selection Tool (V) and hold SHIFT key to make a multiple selection) and set Transparency to Color Dodge and Opacity to 21% in the Transparency window (CTRL+SHIFT+F10).
With the circles still selected, go to Effects > Blur > Gaussian blur and give it a 2 px radius. Hit OK. Now it should look like below.
Create a new circle using the Ellipse Tool (L) like in Step 6. Make it smaller than the first one. Now open the Transparency window (CTRL+SHIFT+F10) and set Transparency to Color Dodge and Opacity to 24%.
Select the circles we created in Step 9 using the Selection Tool (V) - hold SHIFT key to select multiple, then while holding the ALT key, click-and-drag to the top left corner of the square. This will make a copy of what we created in Step 9.
Make more copies and rotate them. Make sure you play around with Opacity until you are satisfied with the results. It should look something similar to the image below.
Select the first circle we created, then copy it (CTRL+C) and paste it to front (CTRL+F). Then right-click > Arrange > Bring to front (CTRL+SHIFT+]). Give it more Blur if you see fit. It should look like below.
Now we'll create a clipping mask so our design would be trimmed nicely.
Copy the background shape and copy it (CTRL+C), then paste it (CTRL+F). Now right-click > Arrange > Bring to front (CTRL+SHIFT+]) and remove its Stroke and Fill.
Select all artwork, then right-click > Make Clipping Mask. And you're done!