The difference between downhill and cross-country skiing is that the cross-country skier can go uphill as well as down.
That capacity is built into the skis he uses, which are narrower and longer than downhill skis.
The skis are in two sections -- the glide and the kick. The glide comes at the forward and aft ends, where the bottom is slick like downhill skis. The "kick" section is in the middle, under foot, where the ski has a grabbing agent built in.
Two grabbing agents are available. On waxless skis the bottoms at the kick are serrated at an angle, so the ski can bite into snow to go forward and glide over it when under way.
Waxable cross-country skis have smooth bottoms but on the middle section, special waxes are used that grip the snow. There are a number of different waxes, differentiated by colors, and each is designed for a particular snow and temperature condition.
Cross-country skis also are bowed lightly in the middle, unlike downhill skis which are flat. That way the kick is elevated except when all the skier's weight is on one foot. When the skier strides forward he puts all his weight on the forward ski, pushing the bow out and engaging the kick.
Cross-country boots are more like shoes than ski boots. They have an extended toe which clips under a simple binding. The heel is free so the skier can lift his foot to push forward.
That has its disadvantages. With no heel binding the skis are difficult to control on downhill stretches.
Equipment notwithstanding, the single most impressive thing about crosscountry skiing is the amount of work that goes into it.