The answer above was spot-on. Please note that if you are shooting in a home studio setting, like against a backdrop or something, your subject might be too close to the background to get much blur.
The blur thing is all about having a narrow depth of field in focus, and then exaggerating it by having a background that is far behind the subject, while the camera is as close to the subject as possible.
Wide lens opening (aperture). This will be controlled by the f/number. Confusingly, a LOW f/number is a WIDER aperture. F/1.8 or f/2.8 would be pretty wide. If you only have the kit lenses that come with a camera you can't hit that low an f/number, so go as low as it lets you. A "nifty fifty" Canon EF 50mm f/1.8 is within anyone's reach. It only costs about $120.00. It feels a bit flimsy but actually has good IQ and a great wide aperture. You will be blown away by the blur you can get.
Distant background. As stated above, if your subject is leaning on a wall or something it will be hard to get much blur. Try shooting outside where you can arrange things so the background is farther behind the subject than the distance your camera is in front of the subject. Another reason shooting outside is a good idea is that the lighting is better and simpler. Flash or studio lighting is complicated for a beginner, and if you are just using the camera's built-in flash you may really make things look worse, with shadows on the wall behind the subject, weird color, and a generally flat washed-out look. If you do shoot outside, just don't do it mid day with the sun directly overhead, which WILL make ugly shots. Shoot in partial shade, or shoot in the hour before sunset or the hour after sunrise (the golden hour).
Long-ish lens focal length. Google a "depth of field calculator". Even if you are shooting with the kit lens 18-55 with a not-so-wide max aperture, you can narrow your depth of field by zooming all the way in to 55mm. Play with the variables you plug into the calculator and you will see what I mean. If you have a kit that goes longer like 18-135 or 55-250, zoom in even farther. Good portrait lens range is considered to be 85mm to 135mm, but that is on a full frame camera. On a crop sensor Rebel everything is magnified by 1.6, so the range is like 50mm to 85mm. If you are outside and have room to back up far enough you can certainly do so and shoot longer than 85mm and it will look good and increase your blur.
Good luck with your new activity, whether it stays for fun or whether you go farther into training and equipment!
Canon 5d mk 4, Canon 6D, EF 70-200mm L f/2.8 IS mk2; EF 16-35 f/2.8 L mk. III; Sigma 35mm f/1.4 "Art" EF 100mm f/2.8L Macro; EF 85mm f/1.8; EF 1.4x extender mk. 3; EF 24-105 f/4 L; EF-S 17-55mm f/2.8 IS; 3x Phottix Mitros+ speedlites
Why do so many people say "FER-tographer"? Do they take "fertographs"?