What are thrust systems ?

Thrusts accomodate shortening as a result of compression (tectonic activity). In general, a thrust fault is more gently dipping reverse fault (less than about 45 degs). A thrust will put older over younger strata resulting in a repetition of strata. Thrust systems contain multiple thrusts as shown on the example interpreted on seismic data from offshore Namibia (Figure 1).

Are they Important ?

Yes, as they often form traps for hydrocarbons.

What are their key characteristics ?

A series of thrust faults across which the various horizons have a reverse offset
Individual thrusts sole onto gently dipping floor thrust.
They can occur at all scales from seismic scale (Figure 1) to hand specimen scale (Figure 2).
Oldest fault is on the right - labelled 1 on Figure 2. The faults become progressively older to the right (from 1 - 4 on Figure 2).
Sometimes the oldest fault has the steepest dip as shown on Figure 2.

Figure 1. Thrust System interpreted on seismic data from offshore Namibia (By Robert Butler, VSA). The black horizon at the top is an unconformity. There is possible some vertical exaggeration on this section hence the dips are not true dips.

Figure 2. Small thrust system in hand sample of sandstone from St Andrews E Beach, UK. Sample collected by Craig Lindsay (Core Specialist Services).

Key takeaways

Thrust systems consistent of low angle reverse faults (dips < 45 degs) which sole out on a more gently dipping, near horizontal floor thrust,
They occur at all scales from seismic scale to hand specimen scale,
They are important as form hydrocarbons traps in many compressional settings.

Useful background on thrusts and structural geology in general..

https://www.files.ethz.ch/structuralgeology/jpb/files/english/4thrustsyst.pdf