Most of the time, we as witches and wizards do not take the time to consider a very important part of casting many spells. The particular words to speak and the wand motions to make are what come to mind, but for many spells we also need to be mentally focused. Mental focus is the ability to close off other wandering thoughts within your mind and focus completely upon the task at hand.

Think of focus like cutting a birthday cake. You don't want to cut yourself with the knife because you were distracted by shouting relatives. You don't want to cut sloppy pieces or smear frosting all over everything. Your goal is a series of neat slices that you can just cut and serve to all of the guests.

At its simplest, focus requires that you are pointing your wand in the right direction so that you don't accidentally cast a spell upon yourself (unless that's what you intended to do). Though rare, sometimes students get lazy and distracted enough to not pay attention to where they're pointing. 

You also don't want to just focus haphazardly upon whatever you're trying to charm. If you're trying to use the Mending Charm but you just casually wave your wand in a general direction without really focusing upon what you're trying to mend and visualizing its unbroken appearance, you may find that it was mended with extra pieces you hadn't meant to fuse together or only partially put back together.

Even if you are focusing upon the specific target of your spell, you must avoid letting stray thoughts get in the way. If you are trying to perform the Severing Charm and you suddenly worry about cutting too deeply, you might find that this is exactly what happens. It is important that you focus only upon what your spell is supposed to do and upon what it is supposed to affect. Some may call this Intent, but in reality focus and intention are the same; you want to affect a specific thing, and you want the spell to work a certain way.

A great way to practice focusing is through meditation. The act of clearing your mind of thoughts and concerns can take considerable effort, but in the long run it will make you a much better spellcaster. You should begin by focusing on your breathing and how the air moves in and out, again and again. Should you have a thought, simply acknowledge that it exists and let it go. This is something that Muggles call mindfulness. By practicing the mental ability to simply let your wandering thoughts go, you will be able to keep them from popping up while you're trying to focus on casting your spell.