Lens distortion is the affect on the image due to the elements in the lens. Often when taking portraits of people this distortion can affect the result which is why wider focal lengths such as 18mm or 24mm are generally not preferred. You often read about 85mm being ideal lens for taking portraits, this is because it is considered to have representation of the real face in the image.
I found this animated Gif on the internet which seems to help you visualise how lens distortion affects the final image in portraits. Below is the breakdown of the Gif so you can see easily the different focal lengths.
Look at the guy’s face at 20mm, it seems squashed and elongated compared to the shot at 200mm where it is appears bigger. His shoulders are wider as well as his hair looks bigger. There is no right or wrong but understanding the capability and limitations of different lens and their focal length can help you create better portraits.
Adobe Photoshop Lightroom or Camera RAW allow you to adjust and remove the distortion affect of many lens, however this is only software correction.
I converted the Gif to a video so you can play/pause it to have better ability to see this. Hope this helps you understand the affects of Lens Distortion, please share with your friends and family.