This is a simple button component which receives an open prop (boolean) and displays a caret icon accordingly to its value. If you want to use it with a dropdown (you probably will), its data-role prop should be set to toggle. The <Dropdown> component takes care of passing down the open prop to the button which has data-role="toggle", so there is no need to do it manually.
<Dropdown
open={this.state.isDropdownOpen}
onToggle={this.onDropdownToggle}
>
<DropdownButton data-role="toggle">
Toggle dropdown
</DropdownButton>
<DropdownMenu data-role="menu">
<span>This is our dropdown</span>
</DropdownMenu>
</Dropdown>