The situation is that you're in a raid and you're healing -- you have a little extra mana and you want to use it to throw debuffs on the main tank's target, but you don't want to miss a second of watching the main tank's bar. Using macros, you can actually cast spells on your focus' target (in this case, your focus would be the MT) without ever changing targets -- just set up a macro to cast the spell, put the button on your bar, and rather than ever having to switch targets, you can just run a macro. You can even use "modifier:shift" and "modifier:ctrl" to switch spells and/or targets. And with simple addons, you can watch your focus target even when you tab away.
Focus is such a powerful tool that it's a little overwhelming to think of all the things that it can make easier in game. But whenever you're in a situation where you're always going back to a certain target (whether that be an MT or self or someone else in the group you're playing with) and can set it as focus, then you can often use macros or addons to make everything else easier after that.