The AppCompat Support Library defines several useful styles for Buttons, each of which extend a base Widget.AppCompat.Button style that is applied to all buttons by default if you are using an AppCompat theme. This style helps ensure that all buttons look the same by default following the Material Design specification.
In this case the accent color is pink.
Simple Button: @style/Widget.AppCompat.Button

<Button
    style="@style/Widget.AppCompat.Button"
    android:layout_width="match_parent"
    android:layout_height="wrap_content"
    android:layout_margin="16dp" 
    android:text="@string/simple_button"/>
Colored Button: @style/Widget.AppCompat.Button.Colored
The Widget.AppCompat.Button.Colored style extends the Widget.AppCompat.Button style and applies automatically the accent color you selected in your app theme.

<Button
    style="@style/Widget.AppCompat.Button.Colored"
    android:layout_width="match_parent"
    android:layout_height="wrap_content"
    android:layout_margin="16dp" 
    android:text="@string/colored_button"/>
If you want to customize the background color without changing the accent color in your main theme you can create a custom theme (extending the ThemeOverlay theme) for your Button and assign it to the button's android:theme attribute:
<Button  
     style="@style/Widget.AppCompat.Button.Colored"  
     android:layout_width="wrap_content"  
     android:layout_height="wrap_content" 
     android:layout_margin="16dp"
     android:theme="@style/MyButtonTheme"/> 
Define the theme in res/values/themes.xml:
 <style name="MyButtonTheme" parent="ThemeOverlay.AppCompat.Light"> 
      <item name="colorAccent">@color/my_color</item> 
 </style>
Borderless Button: @style/Widget.AppCompat.Button.Borderless

<Button
    style="@style/Widget.AppCompat.Button.Borderless"
    android:layout_width="match_parent"
    android:layout_height="wrap_content"
    android:layout_margin="16dp" 
    android:text="@string/borderless_button"/>
Borderless Colored Button: @style/Widget.AppCompat.Button.Borderless.Colored

<Button
    style="@style/Widget.AppCompat.Button.Borderless.Colored"
    android:layout_width="match_parent"
    android:layout_height="wrap_content"
    android:layout_margin="16dp" 
    android:text="@string/borderless_colored_button"/>