Well, it depends on which linguists is using the word today. So welcome to cafeteria linguistics and please choose your mystery meat:
Option 1. It is a Chomskian style parameter which says, all verbs mark for subject and object, or else incorporate the object into the verb.
Option 2 If the language has some valence morphemes (something that shows how many arguments a verb has), then the valence morpheme vary depending on if the arguments are incorporated or not.
Option 3. It is a language with either: lots of morphemes or lots of morphemes per word. The latter sense is more common. Languages with few morphemes are oliogosynthetic.
Languages with few morphemes per word are analytic/isolating. Languages with typically one or two morphemes per word are analytic/isolating, languages with 5-15 are typically called polysynthetic, but as far as I can tell, the split is arbitrary and the middle ground isn’t so clear.
Option 4. It is a language that phonetic rules that allow for merging stand-alone, unbound morphemes (like inserting an u in between stems in compound words in Icelandic), and these rules can be applied a verb plus many other things that otherwise would be unbound, such as subjects, objects, etc.
This idea is somewhat similar to sandhi, where a language’s phonotactics dictate how to change words are word boundaries to make them easier to pronounce– something that happens even for analytic/isolating languages.
Option 5. This is something that American, Inuit and Siberian languages do. With this fuzzy definition, then all sorts of characteristics of American and Inuit verb systems can be called polysynthetic.
What does this mean for conlang design?
It means a feature list isn’t really enough to define your language. You will need to provide explicit examples for each feature and the taxonomy and terminology for what the examples are showing may evolve over time, even if you language doesn’t.