Yup, that's artifacting. As mentioned, the jpeg format is a lossy compression method, meaning some information is thrown away to help keep the file size down. The more you compress it, the more info is thrown away and the worse the artifacts get.
Even the best jpeg compression will throw away some data, and will generate artifacts. The key is to find the balance for a particular picture where the artifacts are least noticeable and the filesize is acceptable. The pictures you attached are particularly bad because of what jpeg is designed for. The algorithm is meant to be applied to 'natural' pictures: landscapes, skintones, etc. Content with harsh or sharp lines such as text always get mangled by jpeg. For these types of pictures, I usually prefer using the png format, it's losless (no information loss), though it generates bigger file sizes.