Haggis is a savoury pudding. 

When one speaks of a "pudding" one does not speak of cream-based sweet desserts such as custard, mousse, rice or Jell-O.  In the United Kingdom and the Commonwealth a pudding could be sweet or savoury.  For example black pudding or a Yorkshire pudding are savoury puddings whereas rice pudding, Christmas pudding or a treacle sponge pudding are sweet puddings. There is a Canadian connection to sweet puddings - the sticky toffee pudding may have origins from two Royal Canadian Air Force Officers billeted in England during the Second World War.

Depending on the type of fat used, a sweet pudding could be a castle pudding (where butter is used) or a college pudding (where suet is used).  This comes from the days when impoverished students could only afford suet fat and the rich ate butter.  For example, the infamous spotted dick is a type of college pudding as it is made with suet as is Clootie dumpling or plum duff.  A Victoria sponge uses butter and is therefore a type of castle pudding - so is sticky toffee pudding.

Many ridicule haggis.  Simply put it is a savoury pudding containing sheep's pluck (heart, liver and lungs), minced onion, oatmeal, suet, spices and salt and stock, all mixed together and encased in a sheep's stomach or artificial casing.  It was known in northern England in the 15th century.  Similar dishes exist in other countries.  And while the traditional casing may sound unappetizing, one should think about the casing on sausages.  As for the contents, the sheep's pluck is simply a form of offal or organ meats.  Liver and onions, pâté, tripe, tongue, steak and kidney pie, blood etc. - all of these are forms of offal and represent the efficient use of animals - from snout to tail.  In Canada's North, this approach is perfectly fine for hunters and especially Indigenous hunters where the efficient use of the animal is not only economical but also respectful to the animal and the land.

There are vegetarian and vegan options for haggis.  These are of course non-traditional.

The haggis is the focus of a Burn's Supper as is the Address to the Haggis, a poem written by Robert Burns:

Fair fa' your honest, sonsie face,
Great chieftain o' the puddin-race!
Aboon them a' ye tak your place,
Painch, tripe, or thairm:
Weel are ye wordy o' a grace
As lang's my airm.

The groaning trencher there ye fill,
Your hurdies like a distant hill,
Your pin wad help to mend a mill
In time o' need,
While thro' your pores the dews distil
Like amber bead.

His knife see rustic Labour dicht,
An' cut you up wi' ready slicht,
Trenching your gushing entrails bricht,
Like ony ditch;
And then, O what a glorious sicht,
Warm-reekin, rich!

Then, horn for horn, they stretch an' strive:
Deil tak the hindmaist! on they drive,
Till a' their weel-swall'd kytes belyve,
Are bent like drums;
Then auld Guidman, maist like to rive,
"Bethankit" hums.

Is there that o're his French ragout
Or olio that wad staw a sow,
Or fricassee wad mak her spew
Wi' perfect scunner,
Looks down wi' sneering, scornfu' view
On sic a dinner?

Poor devil! see him ower his trash,
As feckless as a wither'd rash,
His spindle shank, a guid whip-lash,
His nieve a nit;
Thro' bloody flood or field to dash,
O how unfit!

But mark the Rustic, haggis fed,
The trembling earth resounds his tread.
Clap in his wallie nieve a blade,
He'll mak it whistle;
An' legs an' arms, an' heads will sned,
Like taps o' thristle.

Ye Pow'rs wha mak mankind your care,
And dish them out their bill o' fare,
Auld Scotland wants nae skinkin ware
That jaups in luggies;
But, if ye wish her gratefu' prayer,
Gie her a haggis!

The idea behind a haggis on Burns Night is that the haggis, neaps and tatties, is a fairly wholesome meal but also a humble one - "hamely fare".  It celebrates the austerity and frugality inherent in the Scots' culture.  This is a recurring theme in the poetry of Robert Burns and his pre-occupation with the human condition - some might call him socialist.  Nowhere is this theme clearer than in a commonly recited poem at Burns suppers (and words to a piping tune): A Man's A Man for A'That .  This was revolutionary "stuff" for 1795 and cutting-edge for the time.  

Is there for honest Poverty
That hings his head, an' a' that;
The coward slave - we pass him by,
We dare be poor for a' that!
For a' that, an' a' that.
Our toils obscure an' a' that,
The rank is but the guinea's stamp,
The Man's the gowd for a' that.
What though on hamely fare we dine,
Wear hodden grey, an' a that;
Gie fools their silks, and knaves their wine;
A Man's a Man for a' that:
For a' that, and a' that,
Their tinsel show, an' a' that;
The honest man, tho' e'er sae poor,
Is king o' men for a' that.
Ye see yon birkie, ca'd a lord,
Wha struts, an' stares, an' a' that;
Tho' hundreds worship at his word,
He's but a coof for a' that:
For a' that, an' a' that,
His ribband, star, an' a' that:
The man o' independent mind
He looks an' laughs at a' that.
A prince can mak a belted knight,
A marquis, duke, an' a' that;
But an honest man's abon his might,
Gude faith, he maunna fa' that!
For a' that, an' a' that,
Their dignities an' a' that;
The pith o' sense, an' pride o' worth,
Are higher rank than a' that.
Then let us pray that come it may,
(As come it will for a' that,)
That Sense and Worth, o'er a' the earth,
Shall bear the gree, an' a' that.
For a' that, an' a' that,
It's coming yet for a' that,
That Man to Man, the world o'er,
Shall brothers be for a' that.

It is telling that for the Scots, like their cousins in Ireland and Wales, their national heroes are William Wallace, Robert the Bruce, a flurry of scientists and engineers and poets.