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These terms relate to the trend. Imagine no seasonal variations.
A linear time series has equal increases for every unit of time. So sales for each quarter might go: 1,000, 1,100, 1,200, 1,300 etc. Each quarter increases by 100 and if you plotted these sales on a graph you would get a straight line ie linear.
A non- linear time series has increments which increase (or decrease) Each time period. For example, of sales increase by 10% each quarter you would get: 1,000, 1,100, 1,210, 1,330 etc. Plotting this on a graph would produce a curved line, becoming more and more steep.
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