Contemporary writing is a composition that is set in the ‘here and now’. This is where the setting, characters, and dialogue etc are modern.
For example, in a contemporary setting we would have the technological advances of the day. These would include cars, telephones, and computers to name a few.
The characters would dress in modern clothing such as jeans and sneakers, and would possibly have piercings, modern hairstyles etc.
The dialogue would carry the popular sayings of the day, common words, euphemisms and expressions, such as ‘whatever’, ‘no problem’, ‘babe’, ‘what-the-hell’, ‘Google’, ‘LOL’ etc.
All these things need to be taken into consideration. It is easy to revert to the speech an author may have used in a different era, so the writer needs to be vigilant in these matters when writing a contemporary story.