An organisation or brand's house style is its set of rules for written text. The house style guide will often also include a section on tone of voice.
It is a widely held belief that there are well-established, official, strict rules for grammar and spelling. Most people are aware of the difference between International English (also called British English) and American English, but, within those, imagine that grammar and spelling are fairly settled.
In reality, although the spellings for most common words are fixed, rules of grammar, punctuation and the spelling of new words vary widely from organisation to organisation, and from industry to industry.
An example is how dates are set out. Some people write 7/12/2014, others write 7 December 2014, others 7th December 2014, and others will write the year as '14. All of these are correct (though the short form is easily confused because US dates are in the form month/day/year), but look clumsy and disturbing if used inconsistently within the same document.
Another example is in the use of abbreviations. The UK's National Health Service is officially abbreviated to NHS, not N.H.S., but NHS England is specified in its house style as always to be written NHS England, and never NHSE.
There are variant spellings for many words. Gray/grey are official variants with a long history in the Oxford English Dictionary. Co-operate/cooperate can be spelled either way.
A house style guide is a convenient way of ensuring that all written communications are consistent. This enhances the credibility and clarity of the brand.