Half drop pattern repeats are not as common as they once were, but they still appear from time to time. They are used so that when widths of fabric (or wallpaper) are joined, the pattern looks spread out, without a regular sequence showing up. Here is a brief explanation of how they work.
Straight match with standard pattern repeat
This first graphic shows a normal straight pattern match. The motifs (the horizontal bars) are designed to align when one width of fabric is joined to another. The lengths 'A' and 'B' are cut, and when 'B' is put alongside 'A', the pattern motifs match up.
Half Drop repeat
Now suppose the pattern has been redesigned to using a half drop repeat. Again, the motifs should align when one width is joined to another. But if we do the same as the previous example and just cut the fabric and do a straight join, the motifs do not line up.
The width 'B' needs to be moved up by half a repeat to allow the motifs to align with one another.
By leaving out half a repeat and cutting the fabric as shown below, the motifs on width 'B' now align with those on width 'A'.
But if we now simply carry on with the next width (similar to 'A') and cut it so the motifs align with 'B', we would waste another half pattern. If our curtains had a total of 6 widths we would waste 5 half patterns.
The way to cut lengths is to cut all the odd numbered widths, then move up half a repeat and cut all the even numbered widths.
The blue arrows show how the bottom of width 3 is a continuation of the top of width 1, and the bottom of width 5 is the continuation of the top of width 3. Similarly for the red arrows, which show the the connection for the three even numbered widths.
Notice that the only fabric which is now wasted is the half pattern repeat on width 2.
So cut widths 1, 3 and 5 the same, then move up half a repeat, and cut widths 2, 4 and 6.
If this is something you have never done before, and you want to make sure you cut in the correct places, do the following. We'll assume you're using fabric.
Suppose you need six cuts, as in the example above. Measure off the first three cuts, placing pins or other markers to show where the cuts should be. (These would be cuts 1, 3 and 5 as above.)
Now move along an extra half a repeat, and place a marker at this point. Move this marker to the bottom of the first cut you made, and reassure yourself that the whole cut matches. Measure off the length of a cut and mark the end. Repeat this for the next two cuts.
Doing it this way you can check that all your patterns line up correctly, before you actually make any cuts to the fabric.