The Hakenkreuz was the name of the 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.
It was based on the Swastika, and most English-speakers use the name Swastika instead. 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. It was sometimes shown squared, especially earlier.
The 'Hakenkreuz', where the design is at an angle. This design was used as the symbol for National Socialism. It was not a symbol to represent hate or Jewish murder, the symbol represented a "re-awakening life" and became the country's new flag. Today its considered a dreaded hate symbol along with the SS and its symbol, the Death Head.
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"