Would you believe a FIVE foot radius?
One of the big benefits of clerical magic is the ability to change out spells each day. This gives the cleric some nice flexibility in their magic as well as allowing the player to try out different spells more easily than with an elf or magic-user character. As a result, I think I would have seen even less of this spell in use if it had been an "arcane" offering instead of divine; even though it is only 2nd level. If I had to guess, Bless and Hold Person are probably most people's go-to 2nd level clerical spells. While I have seen Silence used, it's not really that common.
Silence, 15' Radius (Cleric 2)
Duration: 12 Turns
I always used to think of this spell as something the caster would use on themselves or their own party to aid in stealth as opposed to offensively against someone. While both applications are valid, the description focuses more on the latter.
Briefly put, the spell renders anyone or anything inside the area of effect silent. Spells can't be cast, giving verbal orders or conversing normally is impossible and so forth. The effect is normally stationary as well, though it can be cast on an individual so it will move with them. This can be resisted with a saving throw, but even if the target succeeds, the spell will still take effect in stationary form.
For a second level spell, the thing has pretty decent range and duration. Enough so that I could see it being used tactically in a battlefield situation. Not just to mute enemy mages, but to silence a commander trying to order his troops' movements.
Using it to make your party sneakier has the advantage that those inside the effect can still hear what's going on outside the spell's area. DMs would be wise to limit table chatter or players' ability to act upon others' suggestions while the spell is running. If you use command words for certain magical items, it can further limit their options.
Another use for the spell could be for traps or ambushes. Dropping the spell ahead of time in a likely spot, or targeting the PC mage, or a permanent spell effect along a stretch of corridor could make the party very vulnerable in certain situations.