With the new Gmail mobile for iPhone and Android released early this month, Google is adding in more features for the Gmail mobile. A feature called “mute”, which allows you mute a conversation and keep the additional follow up emails for that conversation out of your inbox. ”Mute” was already available on the web version, it is now available on Gmail mobile for iPhone and Android smartphone.

More about “Mute” messages
Muted messages are not marked as read, are still searchable, and can specifically be found by searching for: is:muted
Filters will still be applied to muted messages. To un-mute a conversation, select the conversation and click Move to inbox. Doing so will move the entire conversation to your inbox and will remove the mute action, so that future messages are also delivered to your inbox.