Swiss bank accounts are bank accounts that are tied only to an account number instead of a person's name. This means that no one knows who the account belongs to except for the owner themselves. This secrecy protects the assets of people who are afraid of losing them in some way. Though it's an unintended side effect, Swiss banking is favored by criminals, dictators, and other people who want to make and keep money they shouldn't have. Naturally, El Presidente has a Swiss bank account.
There are many ways of earning private money. The most ethical way is by having people donate to the presidente directly at their childhood museum(s) and mausoleum, but plenty of other, more questionable options are available. Kleptomaniacs will automatically earn money every year from stolen goods and requiring a "Special Building Permit" will effectively allow the presidente to take money straight from the treasury. Other corrupt methods include having banks siphon the nation's money into their pocket, excavating and selling off Ancient Tropican artifacts(3 or 4), and stealing some of the island's export earnings in Tropico 4.
Money that finds its way into the presidente's personal account (instead of Tropico's national treasury) is added to the final score of a game; having a sizable "retirement fund" means that an ex-presidente could potentially get a high score even if they were violently ousted from their position. In Modern Times (Tropico 4), money in the presidente's Swiss bank account allows them to take more corrupt actions, such as having sanatoriums brainwash patients, lacing the island's water with euphoric drugs, or commanding members of SWAT HQs to shoot criminals on sight. However, Swiss bank funds also influence how much revenue is generated by the Babel Tower and are required in order to upgrade the palace into a presidency.