The most important invention of the late 1900s and why?

There's a lot. here are some examples:

Explanation:

1901 : Vacuum cleaner.

1902 : Air conditioning; automated tea maker.

1903 : Electrocardiogram; first powered flight.

1904 : Radar; tea bags; diodes.

1905 : Plastic; windscreen wipers; silencer for guns.

1906 : Radio broadcasting.

1907 : Electric washing machine.

the escalator

Explanation:

because it allowed people who where tired from walking to rest while they were going up the steps