It is usually easier to understand
Silence 
if you understand why and when it is normally used. Examples include:
1) during your opponent's Upkeep (the first time during their turn you can do anything). This stops them casting Sorceries, Artifacts, Planeswalkers, Enchantments or Creature spells that turn. While they can respond with Instants, they havent even had a chance to draw a card yet this turn.
2) before you want to cast an important spell. First, you cast Silence. If they counter it, then that leaves them less able to counter your important spell. If they dont counter it, you wait for it to resolve and then cast your important spell - and they cant even try to use a counterspell against it.
3) in response to a Cascade trigger. Normally
Cascade 
gives your opponent a free spell, but if you cast Silence in response to the trigger, they only get the first spell, not the free one. Best of all, they wont even know that they are only getting the first spell until after they have committed to using it that turn.
4) in response to your opponent using a spell or ability that will give them mana to cast something later on, which isnt actually a mana ability. You cannot respond to your opponent tapping a Forest or a
Llanowar Elves 
for mana, but you can respond to them activating an
Arid Mesa 
, or using
Koth's 
(-2) ability, or to them activating a
Arbor Elf 
.
Silence does have limitations (its not a counter spell, it can be responded to, it doesnt do anything until (and unless) it resolves), but it does have quite potent uses - if you know how to get the most from it.
~ Tim
