Inadvertently is an adjective, meaning that in a sentence, it is used to describe a verb (an action). To to something inadvertently is to do something unintentionally.
For example:
"She inadvertently knocked the vase off of the table as she walked past."
"I inadvertently left the stove on when I left the kitchen."
If you have played "telephone", you know how easy it is to inadvertently garble a message.
I inadvertently mispelled inadvertent "inadvetent", and it made me look like an idiot.
I inadvertently used the wrong word!
I'm sorry, I seem to have inadvertently taken your seat.
Inadvertently I opened your mail, sorry about that.
I inadvertently pooped my pants.
It was clear from the evidence that the damage caused by the fire truck was caused inadvertently, since running over the children's toys was not done on purpose.
I hit him inadvertently.
Have it changed to the proper oil.
Andrew exonerated Emily from thinking that she broke the pendant when he owned up to inadvertently breaking it himself.
No, they will chew endlessly on anything put in their environment and will inadvertently ingest pieces of nylon.
Germany had inadvertently purged its citizens with its economic decline during the industrial time period in America.