Wholesome water is water that is clean, free of dangerous contaminants, and pleasant -- or at least, not too unpleasant -- to drink. In the US this is usually simply referred to as 'drinking water', even in fairly technical documents and in most legislation.
In the UK, and the official and legal terminology is 'wholesome', and water is rated on its 'wholesomeness'. This terminology was also historically used throughout the British Empire, and still is sometimes used in former colonies (and, for some reason, California). Multinational organizations may also use the term, to help maintain clear terminology across boarders.
In the UK the current standards are spelled out in The Water Supply (Water Quality) Regulations 2016, with strict limits on pollutants both chemical and biological. The UK is a bit uptight about water quality, as some older buildings have water tanks that do not meet modern sanitation standards, and must therefore have separate plumbing from the water mains; incidentally, this is historically the reason why the UK maintains the habit of separate hot and cold taps, as the boilers providing hot water would often leach metals into the water, and thus it did not qualify as wholesome.
Generally, clean water, pure water, palatable water, and potable water can be treated as synonyms. However, depending on where you live there may or may not be legal connotations to these terms, so it is worth checking local regulations.