Selection works diffrently depending on what mode you are in; view or edit.
When in edit mode (a text cursor is visible) double tap will select a word. Double tap with two fingers will select a paragraph (though that seems to be broken in iOS 11 Public Beta 2). There are quite a few other special gesture combinatnions to seleect various amounts of text. I forget them all.
Double tapping in view mode (when you can't edit) does not work. Probably because double tapping is reserved for a smart zoom feature. In Safari if you double tap on a colum of text you will be zoomed into that column. Some other apps will do this as well.
In both, you can tap-hold. You'll either select a word directly, or you'll get the context menu that lets you Select (a word) or Select All.