The ground plane is a vertically polarised omni-directional antenna. This makes it good for communicating with mobile stations. That includes working through repeaters such as available above 29 MHz. On frequencies lower than that ground planes are preferred over low dipoles for long distance contacts due to their lower angle of radiation. This is particularly so near the coast due to the beneficial effect on radio signals of large salt water bodies.
Ground planes are one of the best antennas a beginner amateur can build. Especially for bands like 10, 6 and 2 metres. Connecting one to a 2 metre handheld transceiver will greatly increase its communication range compared to the standard 'rubber duck'. And on 10 and 6 metres, even when there's no sunspots, a ground plane will help you work stations thousands of kilometres away over summer.
Check out these practical ground plane links:
Build a Portable Groundplane Antenna Improve your 144 MHz signal - ARRL PDF
Simple ground plane for 2m/1.25m/70cm From N1GY
20 metre three wire ground plane Practical article by KK5JY
10 metre ground plane antenna Video from KG0ZZ
Simple ground plane vertical Video tutorial on a 7 MHz ground plane by W1GV
Find a high support such as a fishing pole or tree branch. Then just get an SO239 socket and some wire to make your own ground plane hanging from your support. Even if radio conditions are poor and you're not hearing many signals, WSPR can give a clue as to propagation and how the ground plane is working relative to your others.
PS: Puzzled about some of the terms you hear? This dictionary can help with over 1500 explained.