die Piste
ski slope
A prepared downhill route for skiing in the mountains.
Nach dem Neuschnee war die Piste in einem perfekten Zustand.
After the fresh snow, the slope was in perfect condition.

slope / runway / track
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ski slope
A prepared downhill route for skiing in the mountains.
Nach dem Neuschnee war die Piste in einem perfekten Zustand.
After the fresh snow, the slope was in perfect condition.

Since 'Piste' has many meanings, context is crucial. Pay attention to signal words: 'Ski' (skis) and 'Schnee' (snow) indicate a ski slope, 'Flugzeug' (airplane) and 'landen' (to land) indicate a runway, and 'Rennwagen' (race car) and 'Kurve' (bend/curve) indicate a racetrack.
Vorsicht, die Piste ist heute sehr eisig!
Careful, the slope is very icy today!
The preposition often reveals the exact meaning. 'Auf der Piste' (on the slope/runway/track) describes a place (skiing, runway), 'auf die Piste gehen' (to go out partying) describes an activity (partying, dancing), and 'von der Piste abkommen' (to go off the track/slope) describes an accident.
Wir waren den ganzen Tag auf der Piste.
We were on the slopes all day.
In skiing, the difficulty of a slope is often indicated with colors: 'blaue Piste' (blue slope, easy), 'rote Piste' (red slope, intermediate), and 'schwarze Piste' (black slope, difficult). People also speak of a 'präparierte' (groomed) or 'vereiste' (icy) slope.
Als Anfänger solltest du nur auf den blauen Pisten fahren.
As a beginner, you should only ski on the blue slopes.
The idiom 'auf die Piste gehen' means colloquially to go out partying. It has nothing to do with skiing or racetracks.
Nach der bestandenen Prüfung sind wir ordentlich auf die Piste gegangen.
After passing the exam, we really went out partying.
This meaning describes an unpaved road. You can recognize it from words like 'Geländewagen' (off-road vehicle), 'holprig' (bumpy), 'Staub' (dust), or from places like 'Wüste' (desert), 'Savanne' (savanna), or 'Dschungel' (jungle).
Die Tour führte über eine staubige Piste durch die Wüste.
The tour led along a dusty dirt track through the desert.
When 'Piste' means the dance floor, it is colloquial. Typical sentences are 'die Piste stürmen' (to storm the dance floor) or 'die Piste füllen' (to fill the dance floor), when many people are dancing.
Als der DJ den Hit spielte, war die Piste sofort voll.
When the DJ played the hit, the dance floor was immediately packed.
course / rate
'der Kurs' and 'die Piste' can both have to do with a route or track, especially in sports or with vehicles. 'Piste' usually means the concrete surface you move on, for example a ski slope or a racetrack. 'Kurs' more often means the direction or planned route that you follow. They can be confused when talking about downhill runs or races. Put simply: you move on a 'Piste'; you follow a 'Kurs'.

Am Wochenende ist die Piste voll, weil viele Familien Ski fahren.
On the weekend, the slope is crowded because many families go skiing.
Das Boot änderte seinen Kurs, weil ein Sturm aufkam.
The boat changed its course because a storm was coming.