A tax class groups products that are taxed the same way — standard rate, reduced rate, zero-rated, and so on. Rates attach to a tax class per zone, so assigning a product to a class is what decides which rates it gets.
The default class
Every market keeps exactly one default tax class; new markets start with one. Making another class the default automatically un-defaults the previous one — there is never zero or two.
Products without a class
The "apply default tax class" setting on the Tax tab decides their fate: while it is on, unclassed products are taxed by the default class; when you turn it off, unclassed products are sold untaxed. The dashboard shows how many products that would affect before you make the change.
Slugs
Leave the slug empty and one is created from the class name — names in any language work. A slug you enter yourself is kept exactly as you typed it; if another class in this market already uses it, saving fails with an error so nothing is changed behind your back.