Vertical blinds rely on a fairly simple adjustment mechanism. However, there are still several things that can go wrong in a vertical blind and jam them when you try to close the vanes. If you pull the chain designed to open and close the vanes and the blinds jam, you need to inspect them and find why they aren't closing properly.
If your blinds get jostled, some of the blinds may twist into the wrong orientation. This causes the other blinds to jam on them when you try to turn them. Make sure that every blind is in the same orientation when open. If they are not, carefully twist the blinds around to correct the problem. If the blind won't twist, you may have to disassemble the blind to correct the problem. Then, try to close them again.
Take the end cap of the blind where the chain enters the blind. If the washer that slides over the rod is too tight, it can bind the mechanism. Loosen this off to help the mechanism move more freely. If the chain still doesn't pull, carefully spray some WD-40 on the gears to loosen everything up. Blinds could seize if unused for a long time, especially if any of the metal parts have rusted.
Installing your blinds improperly can make it impossible for you to open and close the blinds properly. This happens when you don't have enough clearance between the blind itself and the window, window frame or floor. If the blinds are catching at the bottom you may be able to trim the vanes, depending on the material and the manufacturer's recommendations. If they are catching because they are too close to the wall, you need to replace the vanes with a narrower alternative, use a new headrail that puts the blinds farther from the wall, or install extension brackets that place the existing headrail out farther from the wall.
Gear and Stem
If only one of the slats isn't turning properly when you try to close the blind, the gear or stem that holds and controls the slat in place might be damaged. You can purchase replacement units from the manufacturer. Use a pair of needle nose pliers to pull out the stem that holds the vane in place and then remove the gear using the same method. Install the replacements and the slat should close again.