Eldrazi Conscription turns almost any creature into a threat that demands an answer before combat. The enchanted creature gets +10/+10, trample, and annihilator 2. An attack can therefore force two sacrifices even if the creature never deals damage to the defending player, while trample makes blocking with a small creature much less effective.
Eight mana is expensive for an Aura, so decks often look for ways to put it directly onto a creature. Sovereigns of Lost Alara can find it when a creature attacks alone. That creates a huge attacker for damage, although attaching Conscription after the attack was declared is too late to generate annihilator for that particular attack. The trigger will be available on later attacks if the Aura remains attached.
Hexproof and other protection help preserve the investment. A creature that already has evasion can also use the power increase more effectively than one that remains easy to contain. Enchantment decks may value the Aura as a searchable finisher, while a deck with plentiful mana can simply cast it when a threatening attack is available.
Be deliberate about the timing. Removing the creature in response to the Aura can waste a large amount of mana, and summoning sickness still applies after the creature becomes enormous. Choose a carrier that can attack now or that you can protect until the next turn. Conscription is strongest when its arrival changes an immediate combat, rather than sitting on a vulnerable creature and inviting the table to find removal.
