The wording implies an expected increase in conflicts due to the stresses of the time leading up to the end. In other words, amplified contention is a precursor of the end time. His comments specify wars between nations and kingdoms, but John's description in Revelation 6:3-4 expands this out to "people . . . kill[ing] one another." This suggests that this horseman not only deals in mass destruction in civil, border, and world wars, but also in smaller conflicts down to individual murders. Thus, the second seal also covers rising violent crime, gang activity, mob hits, assassinations, family feuds of the Hatfield-McCoy variety, and personal disputes that turn violent.
In saying "wars and rumors of wars," Jesus seems to be saying that some wars will be threatened yet not fought. This is not the sense of the Greek, however. The word translated "rumors" (akoé) is the common Greek word for "sense of hearing" (in the active sense) or "report" (in the passive sense). Jesus really means that we will hear the noise of war with our own ears and we will also hear reports of wars occurring elsewhere. In other words, wars will be taking place all over the world!
Immediately, He cautions us not to let such reports trouble us; that is, He tells us not to let the constant wars cause us to panic. Typically, if a person becomes panicky, his fight-or-flight response kicks in, and his brain shuts down. Our Savior wants us to keep our wits about us because "the end is not yet." Regrettably, war is a natural, human activity, so an abundance of war and violence is not by itself a definitive sign of the end. Certainly, the end time will be one of terrible warfare, but many other factors must fall into place before we conclude that we are living at the close of the age.
Jesus then specifies that "nation will rise against nation, and kingdom against kingdom." Looking at this from today's perspective, we might think He is repeating Himself, but He actually makes a distinction between ethnic warfare ("nation" = éthnos)—wars between different peoples—and political warfare ("kingdom" = basileia)—wars between realms or nation-states. Oftentimes, the former are civil wars within a nation comprised of various ethnic groups, such as the former Yugoslavia. The latter, then, are what we call international conflicts like the recent Gulf Wars. Jesus' distinction tells us that war is the norm both within nations and between them.