This actually has a couple of meanings as an adjective:
to drink lots and generally have a fun noisy time, or
to go from house to house at Christmas singing carols.
I’m going to focus on the second one here. Wassailing was different to carol singing because the singers had a wassail bowl with them – basically a bowl of hot booze, often mulled wine or cider – the contents of which they dolled out to the people they were singing to (why has this died out!?).
There’s also the distinctly pagan-sounding practice of orchard-wassailing, which is when people serenade their apple trees to encourage a good harvest the next year (a custom I’m pleased to say is still alive and well today in rural England).
The word ‘wassail’ itself comes from an Anglo-Saxon greeting: ‘Wæs þu hæl’. This means ‘be thou hale’ and probably morphed into the toast we do to good health today when we’re cheersing (not a word but should be).
Wassailing wasn’t always a wholesome Christmas tradition. Both here and in Europe it was sometimes associated with rowdy yoofs barging into their well-off neighbours’ homes and demanding free food and drink. If the neighbour wouldn’t give it to them, they’d kick up a right old stink, possibly even vandalising their house (think trick or treating without the slutty outfits). This explains the slightly weird bit of ‘We wish you a merry Christmas’. You know, all the stuff about ‘figgy pudding’ and ‘good cheer’ (for which read, booze). The people in the song are refusing to go until they’ve had these (‘We won't go until we get some, so bring some out here’). The bastards.
You can find more Christmas words the English language has forgotten on my blog at http://bit.ly/2URhz6T.
Oh, and happy Christmas y’all.