How do I understand type I error and type II error when talking about hypothesis?

If “one picture is worth a thousand words” then this should help you understand what are type one and type two errors in statistics.

If I would explain otherwise a type I error is the incorrect rejection of a true null hypothesis or a "false positive". The doctor on the left just made an incorrect rejection of his null hypothesis “The man is not pregnant”.

A type II error instead is an incorrect retaining of a false null hypothesis or a "false negative". In fact the doctor on the right just made on incorrect retaining of her null hypothesis “The woman is not pregnant”.