Said of something or someone so unappealing that one wouldn't want to approach near.
Barge-poles are the long wooden poles that are used to push barges along. The term was first recorded in Edward Farmer's Scrap book, being a selection of poems, songs, scraps, etc., 1846:
Barge-pole - A large stick or thick bough. Also generally used for any large piece of wood.
Barges are now less common in the UK, where the word was coined, and those that remain are usually powered by engines. Recreational punting still utilises poles similar to barge-poles.
The earliest reference I can find to the figurative use of 'wouldn't touch with a barge-pole' is Lady Monkswell's Diary, 1893:
It will be a long while before any political party touches Home Rule again with the end of a barge pole.
The expression appears to derive from the earlier American phrase 'I wouldn't touch that with a ten-foot pole'. This is recorded in the magazine of the U.S. Masonic community - The Official Magazine of the Grand Lodge of the United States, 1843, edited by James L Ridgely:
But that mushroom aristocracy of our country... who would not condescend to touch a poor man with a ten foot pole, were their extraction traced, in nine cases out of ten they were nurtured in the squalid huts of poverty.
Ten-foot poles were, in all likelihood, barge-poles by another name.