Crosscuts are backward crossovers, just some skating systems have different names for them.
They are commonly described to look like 'running backwards' when non skaters watch. They're used to gain speed for jumps and spins, and most skaters can gain more speed doing crosscuts than forward crossovers.
The first push is the outside foot, it makes a C shape. The outside foot is the right foot if the skater is doing right over left. Right over left goes in a clockwise circle. Vice versa for left.
The C push is similar to the push learned in backwards half swizzles.
The second push is the underfoot pushing underneath the crossing foot, then lifting and putting in place to prepare for the next C push. The underpush is usually the push that's missing, and judges don't like this because then there's very little power.
Done well, the skater will have a very big, wide C push, with the leg being extended straight at the peak of the C, then a very big, very crossed underpush, with the leg extended straight as it is being lifted. Also, you should barely noticed the underpush leg being lifted. The outside leg stays on the ice at all time.