First of all...
Welcome Aboard,
TheBard!
Glad to have you join the Mac community as well as TS.
We have one very important rule here: There are no dumb questions. Only dumb answers (of which I am the chief supplier). I guess there is a sub-category called "No odd questions" also!
When you first set up a Mac, it usually assumes you are going to be the "Administrator." I'm assuming you have already done that. The second thing, that is important to your question, is that it defaults to 'automatically' log you in on start up. You may not have even seen the option to changes that when setting things up. If you have a desktop machine in a secure area (like your home) that is not a terribly bad setup. But with a laptop, it could be very bad.
Assuming you have your Mac set up and that it is automatically going from power up through its startup routines and ending up with you probably in the Finder, you can still do what the 'tech' people were suggesting. Have the Mac ask for a password or a password and a name or a few other combinations. What this means is that the Mac will
not continue the start up process without those bits of information (mostly).
Open your Systems Preferences ( easiest location is in the "Apple" menu on the far left-hand of the Menu Bar, the Apple logo actually. In System Preferences, look for "Accounts" and open it. If the 'lock' icon is 'locked,' just click it and enter your password. You should now have access to the "Login Options" item. Click that item. At the top of the items on the window is an item named "Automatic login:." Your name probably is showing there. Click on that name and you should see another choice labeled "disable." That's the one you want to prevent the Mac from being completely open to anyone who presses the power button. Below that are several options that will be available on the start up or "Login Screen." Choose whatever you want and close the System Preferences application (in this case you can just click the
red button. Next time you start up, you will be greeted by a small window asking you to select from a list of users and to then enter the password.
That's it!