In Britain what are the "Home Counties?" Why this sobriquet?

I am not 100% sure, but this is my understanding.

It originally refered to English County Cricket's grouping of teams - leagues based around the 'old' central core of the City of London. The teams were based in counties, or districts, either side of the River Thames, which flows lazily, in a winding twisty river channel, through what was the centre of the city.

So, take the 'old' roughly central reference point and with a certain radius, you have a 'circle' of districts. And teams.

The Home Counties are Kent, Surrey (South of the river) and Middlesex and Essex (North of the river.

I think the term has now, in common speech, been extended to include everything within the M25 motorway, an orbital motorway (freeway, or autobahn) that forms a complete ring around London.

BTW, the Home Counties are not to be confused with God's own country, which is Yorkshire and a different place all together