Their are currently 5 terrain types: Plains, Desert, Forest, Water, and Mountain. The terrain attributes of a dinosaur determines on what types of terrain it has an advantage or disadvantage in, whether it's terrain-boosted or if it's neutral. If a dinosaur is fighting in a terrain where it has an advantage (denoted by a Double Circle, ◎), it's Final Stats will be boosted by 20%. If the dinosaur is at a disadvantage (denoted by a Cross, X), it's Final Stats are reduced by 50%. Having Neutral in terrains (denoted by a Circle, O) does not change the dinosaur's stats. Terrain Boosted dinosaurs were introduced in April of 2013. This is indicated by a Star, ★. The Final Stats are boosted by 40%.
Terrain advantages don't give you a very large boost (though it can easily affect the outcome of battle), but the big thing to note are the terrain disadvantages. Considering it cuts your stats in half, It is suggested to stay away from Terrain disadvantages as much as possible. Dinosaurs boosted in certain Terrains are also another thing to note. With a 40% increase in Stats, it could seriously turn the Battle around, and/or make one's Deck even Stronger. Those are the types of Dinosaurs you want most to be in your Deck with, in the right Terrains, of course.
Also, when using the Auto Edit Feature when building a deck, it sorts your dinosaurs based on who will have the greatest amount of Health (it also takes terrain advantages into its calculations based upon which of the 5 terrains you picked). In the deck, a dinosaur which is strong in a certain terrain will give it a +1, neutral has no effect and a disadvantage will give a -1 to the terrain. A terrain boosted dino will give a +2 to the terrain in which it's terrain boosted in.
You are fighting in a water area. Your level 1 Spinosaurus has 1029 HP and 686 ATK usually. Spinosaurus has a terrain advantage (◎) in water areas so while your in that area it gets a boost of 20%.
$ New\ HP=(1.2)*1029=1235 $
$ New\ ATK=(1.2)*686=823 $
Your level 1 Carnotaurus, however, is bad in water areas. So its stats drop 50% from 714 HP and 476 ATK to
$ New\ HP= (0.5)*714=357 $
$ New\ ATK= (0.5)*476=238 $
Your level 1 Rare Excalibosaurus is terrain boosted in water terrain, so its stats increase by 140% from 1450 HP and 1200 ATK to
$ New\ HP= (1.4)*1450=2030 $
$ New\ ATK= (1.4)*1200=1680 $
There are categories to find out which dinosaurs have an advantage in a terrain. Note that some normal dinosaurs do not have a terrain advantage. These categories are useful for forming decks for certain terrains.