What is a Assignment
Assignment is (1) The transfer of ownership or rights through a signature, or,
(2) The notification given to an investor short an option that the option holder has exercised their right and now must meet their obligations as detailed in the option contract.
SecuritiesCE Explains Assignment
When an investor assigns their ownership or rights to another they forfeit that ownership or right.
If an investor is short a call option and receives notice of assignment the investor must be prepared to sell the underlying security at the strike (aka: exercise price) even if the market value of the underlying security is much higher than the exercise price.
If the investor is short a put option and receives notice of assignment the investor must buy the underlying security at the exercise price, even if the market value is considerably lower than the strike price.