Isometric exercise aka 'isometrics' are a type of strength training in which the joint angle and muscle length do not change during contraction (compared to concentric or eccentric contractions, called dynamic/isotonic movements).
Isometrics are done in static positions, rather than being dynamic through a range of motion. The Plank is one of the most popular isometric exercise, as it challenges many core muscles.
Isometric exercises allow for more force generation than concentric exercises because they are not "overcoming" -- you're not actually moving the load, which affects how the cross-bridges cycle (but note that actin/myosin do still cycle during isometric contraction, in humans).
Additionally, isometric muscle action is important to coaches who emphasize the triphasic model of movement because these coaches believe that movement is not eccentric -> concentric contraction, but eccentric -> isometric -> concentric. Thus, these coaches like to train the isometric component of movement.
Furthermore, the Soviet system placed a lot of emphasis on explosive isometric training, again influenced by the triphasic model as well as research that demonstrated some pretty impressive improvements. There were some issues with joint angles and things but I won't get into that here.
The Isometric lifting is a valuable training tool, but it should not be the focus of your training program. Instead, perform functional lifts, which closely resemble athletic movements
I like weighted planks a lot, I feel that they have helped develop my stabilization. I also like using them for smaller muscles: forearms, traps, calves.