The Hakenkreuz is a symbol used by the Nazi Party in Germany, and later by the Third Reich. Adolf Hitler chose it as the symbol of the German Workers Party after he joined. Before Hitler, members had already worn swastika armbands. Hitler was responsible for its red, white and black coloring.
Most English-speakers call it the swastika, even though there's no relation with the Hindu Swastika. The German name comes from the way the arms of the cross (German: kreuz) were crooked, or at an angle (German: haken).
The Hakenkreuz was usually shown at an angle and forward facing. The design creates a dynamic image inside a static box. It was sometimes shown squared, especially earlier.
The Hakenkreuz is at an angle. This design was used as the symbol for National Socialism.
The Nazi party anthem the Horst-Wessel-Lied (English: Horst Wessel's Song) sings about millions of people looking to the Hakenkreuz for hope, in English this is translated as "looking to the swastika"