Invariably describes things that don't change and never vary — they're predictable. Many people invariably start each morning with a hot cup of coffee.
This adverb is useful when discussing things that happen all the time or don't change. In football, teams that win the Super Bowl invariably have a good defense. In schools, many students invariably struggle with writing. Invariably, the weather is hard to predict. In a lot of cases, invariably means always or almost always. You can count on things that are invariable.