A plague wipes out 99-point-something percent of the human race and the survivors have to start again from scratch. The quality of the episodes varies but for me it was never less than good and I'd really put the best ones up there with 'I, Claudius' and the original 'Upstairs Downstairs' at the very peak of classic British TV drama - most notably an episode from the first series revolving around capital punishment and one from the third that's like a cross between a western, a horror movie, The 39 Steps and a Breughel winterscape, with philosophical interludes.
It does have flaws. Some interesting characters are written out too soon, and series stars left without their characters being written out, leading to that unsatisfactory situation I remember from other 70s shows where there are rumours of sightings of them and hints that they may return eventually.
Personally I liked that there was a mix of different types of stories, from adventure to character clash to ideas-based to ones based around technical ingenuity and the resolution of simple problems of coping without infrastructure, even that in the second series there were episodes or portions thereof that were almost idyllic where the major conflict was competing visions of the future. Most of the core characters were middle-class, old-school British, optimists, can-do types, planners, builders, and their belief that they could pull things together again, determination to make the best of things, even excitement at the chance for a fresh start helped make things bearable. But there's plenty of tension, menace, challenge, it's downright harrowing at times, and the deprivations the survivors undergo are a salutary lesson in not taking for granted all the things you tend to. I remember the relish with which I ate an egg after watching an episode where they're an incredible luxury.
If you like (surely the wrong word) John Wyndham's apocalypses or are fascinated by Robinson Crusoe daydreams of 'What would I do if...?' this is especially for you. Avoid the remake like the plague.