What is an adverse reaction or complication caused by vaccine?

The concept of complication corresponds to the concept of "adverse reaction" and is used in the same sense.

Adverse drug reaction – an unwanted and negative response of the body to a medicinal product, that occurs when taking a normal dose of a registered medicinal product intended for the prevention, diagnosis or treatment of a human disease or to restore, correct or modify a physiological function, or any dose of an investigational medicinal product.

The most common adverse reactions to the vaccine (ADR) are local reactions: redness, swelling, soreness at the injection site. More general adverse reactions such as fever, lethargy, restlessness, incessant (unusual) crying, rash, etc., may also occur.
Individual body reacts to each vaccine differently.