When you ignore a channel, this channel can see your posts if it has permission (and if the post you write is also accessible for that channel, for example if you make it public).
But you won't see anything that this channel will post in your network stream, and it won't be allowed to write on your channel (wall or @mention)
To ignore a channel you visit your connection page, from here you select the edit button of the channel you want to ignore. Then Connections tools and from the drop-down menu Ignore.
You can undo the ignore in the same way you ignored a channel.