My PC is an Eldritch Knight. I was wondering what is an Arcane Focus? Do I need to have it in my hand? If I get the War Caster Feat does my arcane focus become obsolete?
As an Eldritch Knight, you cannot use an arcane focus. The description for the arcane focus includes this clause:
A sorcerer, warlock, or wizard can use such an item as a spellcasting focus, as described in chapter 10.
If that wasn't enough, the descriptions for a sorcerer's, warlock's, or wizard's spellcasting all include a matching clause allowing them to use an arcane focus:
You can use an arcane focus (found in chapter 5) as a spellcasting focus for your sorcerer spells.
So if you want to cast a spell that has a material component, you will have to use a component pouch, not an arcane focus. As for War Caster:
You can perform the somatic components of spells even when you have weapons or a shield in one or both hands.
This means that you can perform somatic components with your hands full. However, this does not affect your use of material components in any way. Unfortunately for you:
A spellcaster must have a hand free to access these components, but it can be the same hand that he or she uses to perform somatic components.
So if you want to cast a spell that has a material component, not only will you need to use a component pouch, you will also have to have an empty hand to do it with.