Some form of Battlefield appears during every dinosaur battle in the anime. They are only brought on when at least one of the combatants feels some aggressive attitude towards another. All battlefields involve some visual alteration from the "regular" appearance of the surrounding landscape, often with color changes or partial to total CGI replacement. They are used by the D-Team to tell when there is a dino battle going on nearby early in the show (episode 7), but references to them largely disappear by the halfway point of Series 1 (though a stray mention is as late as episode 38). Dr. Taylor's Japanese dialogue from episode 1 shows he believes them to be a warping of time and space, but the English dub never addresses their origin.
During a Regular Battlefield, all the colors of the landscape and sky turn into blue, purple, and pink with an oil painting-look resembling the day turning into dusk. They appear only in Series 1, and they gradually transition into and are eventually replaced by Partial Battlefields described below towards the end of Series 1. Many of these battlefields after the first few have the same sky pattern as Partial Battlefields.
Partial Battlefields involve the sky turning to a pulsating yellow, orange, green, and purple pattern, looking almost like a soap bubble. The landscape changes somewhat so as to look almost CGI, or at least be obviously visually different from the "normal" animation style from the audience's point of view, but there is rarely any major change in color. They first appear near the end of Series 1 and are the only type of battlefield seen in Series 2.
Time Warps are special battlefields that appear occasionally throughout Series 1 (starting in Downtown Runaround), mostly during "big" dinosaur battles. They involve the entire surrounding landscape being completely replaced by one of various CGI landscapes (a forest, a clearing in front of a lake with a waterfall, a barren rocky landscape in front of a sometimes active volcano), all with the same "soap bubble" sky as the other battlefields. Sometimes, other forms of battlefields become Time Warps when additional dinosaurs are summoned (like in Tee'd Off). Characters liken Time Warps to being transported elsewhere, as anyone/thing not a fighting dinosaur, controlling a dinosaur, or standing nearby won't join them in the battlefield; it's not known what someone not included in this would see from a distance.
It is to be noted that many of the Time Warp locations seem to come from the generic CGI Mesozoic region of "Dinosaur World".
These Elemental Battlefields aren't really "battlefields" in the same sense as those described above. They appear in many, but not all, cases when dinosaurs are using a Move Card. They involve the entire landscape being replaced by a blue/purple-tinged stone ground extending infinitely in all directions, with the sky being black with fog/clouds colored like the Element of the dinosaur using the Move. When a Space Pirate-controlled dinosaur is using the Move, the sky is entirely dark purple and pink, with no black visible. When an Ultimate Move is being used, the stone ground is replaced by circuitboard-looking blue and green lines with small circles on the end. In Fate of the Cosmos, there is a version of this with red and purple lines when the Space Pirates' main dinosaurs use their Spectral Moves. This version was surprisingly first seen in Lights, Camera, Destruction! as a Hollywood green screen background when Pentaceratops was fighting Terry.
These Elemental Battlefields are in no way related to the Lightning, etc. Battlefields appearing in the DS Game.