What a linear calendar is
A linear calendar lays the whole year out as one continuous strip of time instead of pages: the twelve months as rows, one under the other, every day a column - 1 January top left, 31 December bottom right, everything in between visible at once. Some versions align the days by date, some by weekday, some turn the whole thing on its side; the three layouts are below.
The ordinary calendar does the opposite: a grid calendar gives each month its own page, and an app shows a day, a week or a month and keeps the rest behind a scroll. The linear calendar keeps the year in one piece - that is the whole idea. A plan is no longer a note on a day but a bar with a length, and the year is a line you can read from end to end.
The idea is not new. In Germany the year on one sheet has hung in offices for decades as the wall planner, and Roman walls carried the whole year in columns two thousand years ago. What is new is the name - and that you can now plan in one instead of just looking at it.