Hogmanay is the Scots name for New Year's eve.
The tradition of seeing out the old year and welcoming in the new has, in cities such as Glasgow and Edinburgh, been adopted and transformed in recent decades to the point that 'Hogmanay' is now often associated with these huge public type of 'events' with firework displays. However many older non-commercial public events take place around Scotland e.g. the Stonehaven Fireball Festival or Comrie Flambeaux.
Prior to the recent 'Edinburgh's Hogmany' festival which has successfully attracted tourists from all over the world to the city, 'locals' used to gather in the High Street/Royal Mile in the area of the Tron kirk to wait for its bells to ring at midnight (accompanied by impromptu dancing of reels etc in the open area outside St Giles Cathedral - see Heart of Midlothian )
The less public side of Hogmanay was marked amongst and with friends, family and neighbours. Listed below are some of the traditions and rituals still carried out, the main feature of which consisted of visiting the houses of friends' and relations to 'see in the bells' (the ringing of church and other bells to mark midnight on New Year's eve). Public rituals still take place which are neither 'organised' or commercial. For example in coastal, harbour or other areas where there is shipping (formerly the Clyde shipyards) boats or ships sound their horns at midnight.
The main Hogmanay ritual still practiced by some is First-footing. This has also evolved over the decades but the main premise is that the first person crossing the threshhold of your house after the bells should bring good luck for the new year. A dark stanger (often a coal-man or chimney sweep) would be extremely good luck, but if none is available, the person 'first-footing' you should at least be carrying a lump of coal, a piece of Black Bun (see culinary traditions) and a bottle of whisky (fuel, food and drink). This is still carried out to various extents e.g. Rosemary from Glasgow takes the same lump of coal first-footing with her that her father used when he was alive (it's now 'all shinywith no soot on it'!).