I’ll just add more examples for some parts since other people explained it pretty well.

The triple bar for equivalence is especially useful for modular arithmetic. An example of that is on a clock, 4 am and 4 pm are equivalent so comparing 24 hour time to 12 hour time, 4 is equivalent to 16 (mod 12).

A logical biconditional means “if and only if” so the two things necessarily mean the other is true. A shape is a triangle if and only if it has exactly 3 sides. That means that any shape with exactly 3 sides is a triangle and a triangle has exactly 3 sides.