Invariably means always, without exception, or in every single case. If something happens invariably, it happens every time without fail.

When your teacher invariably starts class at 8:00 AM, she never begins at 8:01 or 7:59: it's always precisely on time. When a scientist observes that heated metal invariably expands, she means it happens in every experiment, no matter what. If your friend invariably forgets his lunch on Mondays, he literally never remembers it on that particular day of the week.

You'll often see this word used to point out patterns: “The fastest runner invariably wins our relay race” means that the fastest runner always wins. Writers use invariably when they want to emphasize that something truly happens without exception, not just usually or often. It's stronger than saying “almost always”: when something occurs invariably, there are no exceptions to the pattern.