The phrase "tutorial quest" refers to a step-by-step guided mission or activity designed to teach someone how to do something new or learn a skill. Full definition
You get a decent amount of money fulfilling tutorial quests so it's recommended you do them. (mypotatogames.com)
In a later tutorial quest, you will be visiting the supermarket so that you can buy a pet bowl and pet food. (mypotatogames.com)
After a new expanded tutorial quest chain — an interesting and canonical diversion that vastly improves the new player experience — you'll settle into a routine of picking missions from a massive list of different planets from your space ship hub, at which point you'll be grouped together with three fellow Tenno and sent into battle. (dealspwn.com)