Random Encounters
Random Encounters, enemy encounters that occur suddenly when traveling on foot or in some vehicles, are a recurring element of the Dragon Quest series. As indicated, random encounters can occur at any time when walking on the overworld or in a dungeon. As of Dragon Quest IX they have since been replaced by visibly seeing enemy encounters on the geography being explored.
Mechanics
The enemies a player can meet varies both on where they are in the game and the terrain they are on. For example, the forest may contain enemies not found in the plains. For games that include travel by ship, enemies encountered while at sea are from an entirely separate set. Some enemies have a very low encounter rate and thus are almost impossible to find; these usually give out large amounts of Experience Points or some other significant reward, the most obvious example being the Metal Slime.
Abilities such as Taloon's Padfoot enable players to avoid or reduce the probability of Random Encounters if the player does not wish to fight in order to save time or HP. Random encounters can be prevented all together for a short time through use of the Holy water item or the spell Holy Protection. In the games that it's available in, the Gospel ring when equipped by a currently active character will remove random encounters altogether.
Similarly, if one wishes to battle more (perhaps for EXP), he or she might use other abilities increase the probability of having a Random Encounter, or, such as in the case of Whistle or the Silver Harp, cause one immediately. As an opposite of Holy water, use of Musk or Monster munchies will increase the random encounter rate.
In Dragon Quest IX, the mechanics had a significant change: encounters are now initiated by interacting with monsters on the field. While the actual contents of the encounter can still vary like before, the overworld model indicates what you'll be dealing with, and it's possible to avoid these encounters. Some however might charge at the party or give chase upon spotting them, making Vanish useful for avoiding detection. Initiating an encounter when the monster's back is turned increases the chances of getting the first strike (and vice versa, if the party is chased). The one exception to all this is ship travel, which uses the same mechanics as previous games due to the scaled down world map.
