Existing text-based tables in a buffer, which lack the special text properties applied by M-x table-insert, are not treated specially as tables. To apply those text properties, type M-x table-recognize. This command scans the current buffer, recognizes valid table cells, and applies the relevant text properties. Conversely, type M-x table-unrecognize to unrecognize all tables in the current buffer, removing the special text properties and converting tables back to plain text.
You can also use the following commands to selectively recognize or unrecognize tables:
See Table Conversion, for another way to recognize a table.