The "Reduit" (retreat) area in blue
Traditionally neutral Switzerland is very concerned about the outbreak of World War II, especially since the Nazis talk a lot about annexing the "germanic" part of Switzerland. Their worries grow even more, when the Nazis invaded the - also neutral - States of the Netherlands, Belgium, and Luxembourg. This is why the government called for Geistige Landesverteidigung (Spiritual national defence), the Army mobilised no less than 430,000 men (for a country of 4.2 million people) as early as the second day of the war, and the Military under General Henri Guinan and his chief of Staff Samuel Gonard worked out a Plan to never surrender, but continue the defense in the extremely well fortified "Reduit" (National Redoubt) - which is stronger than either the Maginot Line or the Siegfried Line. British General Bernard Montgomery called the Reduit a nonsense however. While he doesn't know, for a small part of the bunkers, there was material used which wasn't exactly first-class.
The Luftwaffe didn't mind crossing Swiss airspace much, which is why the Swiss had to shoot down several planes since the beginning of the western campaign, and Germany protested diplomatically in early June 1940.
During June 1940, about 40,000 Allied Soldiers, mostly Frenchmen and Poles, crossed the Swiss border, to be interned. After the Fall of France and the Establishment of Vichy France in June, Switzerland is completely surrounded by the Nazis and their allies/collaborators, which makes its Situation a very difficult one.
It's also concerning that some Colonels within the Swiss Army have sympathies for Nazi Germany: notably Arthur Fonjallaz and Eugen Bircher, who led the Schweizerischer Vaterländischer Verband.
See also: Liechtenstein