The Dragon Balls, numbered 1 through 7, when collectively gathered, can be used to summon the eternal dragon who can grant wishes to the summoner. The Dragon Balls were originally created by the Namekians.
There are four different sets of Dragon Balls in total. There are the Earth Dragon Balls, Namek Dragon Balls, the Super Dragon Balls, and the non-canon Black Star Dragon Balls. Each set of Dragon Balls can grant wishes, but their power and appearance differ slightly from the other balls. If the creator of a set of Dragon Balls dies, the Dragon Balls will turn to stone and become useless unless they are restored by another Namekian, or the creator is brought back to life.
Earth's Dragon Balls
The Earth Dragon Balls were made by the Namekian, Kami, when he traveled to the planet Earth. Once used, they are turned into stone, and cannot be used unless revived by Kami, or another Namekian for one year. If only one wish is granted, they can be located again in four months time. Once used, the dragon balls disperse across the planet and must be found again.
The Earth dragon balls summon the eternal dragon Shenron. He can grant one wish. When he was revived by Dende, he could grant two. He can only revive a person from death once.
The first Dragon Ball introduced was the "4 Star" ball. It was carried by Goku through much of the original Dragon Ball series. It was said that the "4 Star" ball held the spirit of Grampa Gohan, his adoptive Grandfather. These Dragon Balls could be found using the Dragon Radar, an invention made by Bulma Briefs of Capsule Corporation.
Namekian Dragon Balls
There are also seven dragon balls on the planet Namek, home of their origin. They are much larger than the Earth dragon balls. They summon the eternal dragon Porunga, who is capable of granting three wishes and has no limitations on reviving the dead, although he can only revive one person at a time. After Namek's destruction, the Namekian dragon balls followed the Namekians to their new home.
Not only does Porunga grant more wishes than Shenron, he can also be summoned every 130 days, as opposed to Shenron's full year.
Super Dragon Balls
Dragon Ball Super introduced the Super Dragon Balls that are each the size of a planet and are scattered throughout the universe. Champa stated the Namekians took pieces of them to create their Dragon Balls. The Super Dragon Balls are also said to be able to grant any wish.
Black Star Dragon Balls
The Black Star Dragon Balls are an anime only set of Dragon Balls introduced in Dragon Ball GT. Cosmetically, these Dragon Balls look nearly identical to the more commonly seen set on Earth with the only difference being the stars adorning the surface are black rather than the typical red stars. The Black Star Dragon Balls are said to be much more powerful than both the Earth's Dragon Balls and the Namekian Dragon Balls.
Ultimate Shenron, the dragon of this set, looks very similar to Shenron. The only differences are that Ultimate Shenron is red and is significantly larger. His head is larger than Kami's Lookout. He is said to have no limits on his wish granting capabilities.
To offset the incredible power of the Black Star Dragon Balls, they are restricted to only one wish and after that wish the balls are scattered throughout the universe. If the balls are not all returned to their host planet after one year, the planet will explode. For this dangerous reason they were kept sealed away in Kami's Lookout for many years.