It essentially means something that doesn't matter much, or that has a very small impact.
Here are some synonyms for inconsequential:
* Trivial
* Minor
* Unimportant
* Negligible
* Meaningless
* Insignificant
Here are some examples of how "inconsequential" can be used:
* "The argument was about something inconsequential, like who was going to wash the dishes."
* "The mistake was inconsequential and didn't affect the outcome."
* "I feel like my work is inconsequential to the overall project."