You can use it to lighten the font essentially. But it's more than that.
In some cases, you might want a more transparent (or lighter) version of a font, but may not know (or want to specify) the current (or hard-coded) font color. The current font might be white, red, green, or anything. So setting the alpha will lighten the font towards transparent, in the current font's color.
<font alpha="50">
is 50% of full saturation. Really what it means is how much of the background should bleed through (aka alpha channel, blending), or how opaque the text should be.
Try pasting this into the Expanded template for the TV Show caption, and then mousing over items in Theater View:
<font alpha="100">A 100 </font><font alpha="90">A 90 </font><font alpha="80">A 80 </font><font alpha="70">A 70 </font><font alpha="60">A 60 </font><font alpha="50">A 50 </font><font alpha="40">A 40 </font><font alpha="30">A 30 </font><font alpha="20">A 20 </font><font alpha="10">A 10 </font><font alpha="0">A 0</font>