In this diagram about the methane concentration in the martian atmosphere, there are data points labeled "Mars year 32", "Mars year 33", and "Mars year 34". How are Mars years counted? Is there a "Mars year 0"? What is the event that defines the start of the time scale?
Given that the methane variations are seasonal, the diagram is labeled in Martian years - the amount of time it take Mars to travel around the Sun once (about 1.88 Earth years). This makes it much easier to see the cycles rather than using Earth years. In particular, the x-axis has a length of one Martian year; the data point show seasonal methane measurements for that year. So, for instance, the red data point was take early in the spring of Mars year 34, the first blue point was taken at the start of summer of Mars year 32 (earlier!), and so on and so forth.
The specific year numbering is an arbitrary convention begun on April 11, 1955 (the northern spring equinox). The solar longitude system is applied to Mars; it's a geometric way of describing where in its orbit a planet is. The solar longitude is denoted $L_2$; on April 11, 1955, $L_s=0^\circ$; it increases to $L_s=360^\circ$, at which point a new Martian year begins.