Not to be confused with annotations, connotations are those associations we create with certain words. This is actually the basis of word-association games, is working off those connotations to create a chain of words which would be otherwise, seemingly unrelated.
For writers, connotations are a powerful tool to use, especially when dealing with symbolism. Often when told to think of good versus evil, you might think of light and dark. These are common connotations created by the repeated used of symbols across multiple forms of media. You’ve probably heard the phrase ‘doom and gloom’ at least once or twice before, and likely know the ‘knight in shining armor’ is probably supposed to be a good guy. Those are connotations at work.
Connotations can often help in making appropriate word choices. Floral and flowery are both words with definitions meaning ‘of or full of flowers’. However, floral often refers more to patterns, where as flowery is used more to refer to scents such as someone’s perfume, or handwriting. Saying floral wallpaper brings to mind the idea of actual flowers printed on the aforementioned wallpaper. Flowery wallpaper by contrast might bring up the idea of designs resembling flowers without being identifiable as any specific flower.
However, connotations are also built up in individuals by past experience. Depending on what you’ve been through, hearing the bang of something small exploding nearby might make you look for fireworks, or duck for cover from what you presume is gunfire. In reality, that same sound can also be caused by popping an air packet from a shipping container, or a car backfiring. This occurs too with words. Some see the word ‘gelatin’ and think of sweet desserts, but others might think of wiggly, flavorless goop.
When in doubt, try asking a few people for what they think of when they hear a particular word or phrase to see if you’re coming up with the right words to fit what you need. Aim especially for people of your target audience if you have one, and see what their thoughts. Chances are strong that they can help you spot problematic connotations and pick more appropriate words.