I am playing Minecraft 1.7.2 with OptiFine and ShadersMod
On the achievement box I saw this button. What is purpose of this button? When I click the button only the 'button click' sound plays.
Some additional mods have their own achievement lists. This button switches between them. Eg, if the button says "Minecraft" it is showing the Vanilla achievement list. If it says, perhaps "IndustrialCraft" (a different mod), it will be showing the IndustrialCraft achievements.
However, because the mods you currently have do not add anything else to the game, this does not have any other unique achievement lists.