What does the WPF star do (Width=”100*”)

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In a WPF Grid, Width="*" or Height="*" means proportional sizing.
For example: to give 30% to column 1 and 70% to column 2 –

<ColumnDefinition Width="3*" />
<ColumnDefinition Width="7*" />

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And likewise for rows –

<RowDefinition Height="3*" />
<RowDefinition Height="7*" />

The numbers do not have to be integers.
If the Width for RowDefinition (Height for ColumnDefinition) is omitted, 1* is implied.
In this example, column 1 is 1.5 times wider than column 2 –

<ColumnDefinition Width="1.5*" />
<ColumnDefinition />

Column 1: 1.5*, Column 2 1* (implied)

You can mix auto-fit and fixed widths with * (proportional) widths; in that case the * columns are apportioned to the remainder after the auto-fit and fixed widths have been calculated – 

<Grid.ColumnDefinitions>
    <ColumnDefinition Width="Auto" />  <!-- Auto-fit to content, 'Hi' -->
    <ColumnDefinition Width="50.5" />  <!-- Fixed width: 50.5 device units) -->
    <ColumnDefinition Width="69*" />   <!-- Take 69% of remainder -->
    <ColumnDefinition Width="31*"/>    <!-- Take 31% of remainder -->
</Grid.ColumnDefinitions>
<TextBlock Text="Hi" Grid.Column="0" />

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