Button dropdowns are useful when you need a button that can perform multiple related actions. For example, you could have a save button that saves a record, but you would also like to give the user an option to save the record and automatically show a new empty form to create another record. This will be beneficial to the user when they need to create multiple records of the same type.
For example, the following code creates a button dropdown inside a form that will create a save button with two additional actions:
<div class="form-group">
<div class="col-sm-offset-2 col-sm-10">
<div class="btn-group">
<button type="submit" class="btn btn-primary btn-sm">Save</button>
<button type="button" class="btn btn-primary btn-sm dropdown-toggle" data-toggle="dropdown">
<span class="caret"></span>
<span class="sr-only">Toggle Dropdown</span>
<...