While iOS is quite powerful, it still cannot natively take a .zip file and unzip its contents. My go-to app is Zipped. It's only $1, and it does exactly what I need it to do. You can take a .zip file and extract it to the Files app. It also supports drag and drop on the iPad. You can also create zip files from a collection of files as well.

It currently supports zip, .png, .jpg, .html, .pages, .docx, .pdf, .numbers, .xlsx, .pptx, .rtf, .txt, .mp4, .mov, .aiff, .mp3, .wav, .psd, .caf, .md, .csv, .json, and .js files.

Get it on the App Store for $1.