Enhancing will strengthen your followers. Select the Follower that you wish to Enhance (Enhance Knight) and merge it with another Follower (Material Knight). The Material Knight will disappear after Enhancement so be careful when you choose! Identical Followers cannot be used for Enhancement.
You can select up to 10 Followers at one time to do a Batch Enhance. But, Knights above a certain Rarity, and/or Lv will not appear in the Batch Enhance section. Since Material Knights disappear permanently when you Enhance, this is to prevent any accidental picking of those Rare Knights that you have worked so hard to get.