Inside - Outside

• gravity arranges the content inside the view.
• layout_gravity arranges the view's position outside of itself.

Sometimes it helps to see a picture, too. The green and blue are TextViews and the other two background colors are LinearLayouts.

Notes

• The layout_gravity does not work for views in a RelativeLayout. Use it for views in a LinearLayout or FrameLayout. See my supplemental answer for more details.
• The view's width (or height) has to be greater than its content. Otherwise gravity won't have any effect. Thus, wrap_content and gravity are meaningless together.
• The view's width (or height) has to be less than the parent. Otherwise layout_gravity won't have any effect. Thus, match_parent and layout_gravity are meaningless together.
• The layout_gravity=center looks the same as layout_gravity=center_horizontal here because they are in a vertical linear layout. You can't center vertically in this case, so layout_gravity=center only centers horizontally.
• This answer only dealt with setting gravity and layout_gravity on the views within a layout. To see what happens when you set the gravity of the of the parent layout itself, check out the supplemental answer that I referred to above. (Summary: gravity doesn't work well on a RelativeLayout but can be useful with a LinearLayout.)

So remember, layout_gravity arranges a view in its layout. Gravity arranges the content inside the view.

xml

Here is the xml for the above image for your reference:

<?xml version="1.0" encoding="utf-8"?>
<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    android:orientation="vertical" >

    <LinearLayout
        android:layout_width="match_parent"
        android:layout_height="0dp"
        android:layout_weight="1"
        android:background="#e3e2ad"
        android:orientation="vertical" >

        <TextView
            android:layout_width="wrap_content"
            android:layout_height="wrap_content"
            android:layout_gravity="center_horizontal"
            android:textSize="24sp"
            android:text="gravity=" />

        <TextView
            android:layout_width="200dp"
            android:layout_height="40dp"
            android:background="#bcf5b1"
            android:gravity="left"
            android:text="left" />

        <TextView
            android:layout_width="200dp"
            android:layout_height="40dp"
            android:background="#aacaff"
            android:gravity="center_horizontal"
            android:text="center_horizontal" />

        <TextView
            android:layout_width="200dp"
            android:layout_height="40dp"
            android:background="#bcf5b1"
            android:gravity="right"
            android:text="right" />

        <TextView
            android:layout_width="200dp"
            android:layout_height="40dp"
            android:background="#aacaff"
            android:gravity="center"
            android:text="center" />

    </LinearLayout>

    <LinearLayout
        android:layout_width="match_parent"
        android:layout_height="0dp"
        android:layout_weight="1"
        android:background="#d6c6cd"
        android:orientation="vertical" >

        <TextView
            android:layout_width="wrap_content"
            android:layout_height="wrap_content"
            android:layout_gravity="center_horizontal"
            android:textSize="24sp"
            android:text="layout_gravity=" />

        <TextView
            android:layout_width="200dp"
            android:layout_height="40dp"
            android:layout_gravity="left"
            android:background="#bcf5b1"
            android:text="left" />

        <TextView
            android:layout_width="200dp"
            android:layout_height="40dp"
            android:layout_gravity="center_horizontal"
            android:background="#aacaff"
            android:text="center_horizontal" />

        <TextView
            android:layout_width="200dp"
            android:layout_height="40dp"
            android:layout_gravity="right"
            android:background="#bcf5b1"
            android:text="right" />

        <TextView
            android:layout_width="200dp"
            android:layout_height="40dp"
            android:layout_gravity="center"
            android:background="#aacaff"
            android:text="center" />

    </LinearLayout>

</LinearLayout>

Related

• Difference between a View's Padding and Margin
• Match_parent vs wrap_content
• How to set both gravity and layout gravity of a LinearLayout programatically