The Ancient Watcher is a 2 mana minion with 4 attack and 5 health. That's pretty beefy for a 2 mana minion! There's a catch: it can't attack. In a druid deck with a pair of Keepers of the Grove and an Ironbeak Owl for good measure, that obstacle is easily overcome. Silencing the Ancient Watcher removes its restriction, turning your 2 mana minion into a powerhouse. It's unlikely you'd want to silence your own minion rather than one of your opponent's, but the opponent has nothing worth silencing, it's better than wasting it.
Considering you can get that onto the field by turn 3 if the draws are in your favor, that's one hell of a tank to have on the field so early. If you're lucky, you can pile them both on. Your opponent will have no choice but to use their Polymorph, Hex, Assassinate, or so forth to break through it. Their other option us to use a silence, stripping away the Ancient Watcher's buffs ... and its Can't Attack restriction. They may have eliminated its ability to absorb damage for you, but they've unshackled a 4/5 threat.
It's also worth keeping in mind how buffs and silences work in Hearthstone. When a minion is silenced, that doesn't mean it can't ever be buffed again. A silence only removes its current buffs and debuffs. If you play the Ancient Watcher and Silence it, giving it the ability to attack like any other minion, you can apply Mark of the Wild to create a 6/7 tank with the ability to attack. If your draws are perfect, that super-powered Ancient Watcher will be on the field long before you could typically play a minion that strong.
Again, though, this isn't likely to be competitive. There are too many cards in the game that can outright neutralize a single, powerful minion. You could easily dedicate 3-4 turns to buffing up the Ancient Watcher only for it to be destroyed by a Deadly Shot without putting up a fight. It's simply a fun combination in the right deck and will sometimes catch your opponent by surprise. I've played against friends who giggled when they saw I played what appeared to be a completely useless minion, only for me to wreck their face because they weren't prepared to deal with the end product.
In any case, the Ancient Watcher forces your opponent to make some tough decisions. Early in the game, it's unlikely they're well-equipped to eliminate it quickly and easily. However, if they ignore it too long, it could turn into the most dangerous thing on the field.