You can use ten of the same gemstone, plus 20 Meteorite Bars, to craft a phaseblade. All phaseblades are identical except for color, which is based on the color of the gemstone. You only need ten total gemstones, all of one type. You do not need ten of each.
As of 1.05, they have other uses! Six to ten each of two gemstones are required to craft Jungle Armor set pieces. You will need ten emeralds and sapphires, eight amethysts and topaz, and six rubies and diamonds. (for a total of 48 gemstones.) Additionally, rubies are used to create the Robe and Gold Crown, while topaz are used to create the Sandgun. (Source: http://wiki.terrariaonline.com/)
As of 1.1, each of the gemstones can be combined with 3 torches to produce 3 colored torches (shows off Terraria's new lighting engine!).
As of 1.2, each of the gemstones has an associated ore that it can be crafted with to create a "___ Rod" item, which is a rod made out of 15 of your gemstones and 10 bars of a particular ore. The Diamond and Ruby rods are First-and-second best, and use Platinum and Gold bars respectively.
All gemstones can now also be used to craft new grappling hooks that don't require a Hook to create, making them ideal for new characters. The Ruby and Diamond hooks also have a longer reach than the Ivy Whip.
In addition, these gems can be used to create Large Gems for the Capture-The-Flag game, so it would be wise to hold onto some in case you ever wish to host said game for some of your friends.
There is no single official end goal. However, there are a few long-term goals the game sets:
- Fight all boss monsters (kind of the minimum thing you have to do before you can claim to have beaten the game)
- Get/craft all equipment (requires fighting many bosses multiple times).
- Completely eliminate all corruption from the world (the Dryad wants you to do this, but it would be an incredible amount of repetitive work).
- Collect all achievements.
And of course you can do all this in mediumcore or hardcore for an extra challenge.
Apart from that, many players make up goals for themselves, often in the form of building elaborate structures.
Best Answer
Those particles appear if you have a summoned minion (such as the Imp or the Hornet) and you have right-clicked on the monster while holding the summoning tool. Three small purple particles will revolve around the monster you clicked, and your minions will try to focus on that target instead of any other nearby enemies. This is useful in boss fights where the boss summons a bunch of smaller monsters (such as the Eye of Cthulhu or the Wall of Flesh), since it increases your DPS against the biggest threat.
This is a new feature in 1.3.4 - prior to this version, minions would simply attack whatever enemies were closest/easiest to reach.
Edit:Further info: While playing around with the summoning items, I did notice that often you don't even have to click directly on a monster - it's quite possible that you had the summoning staff equipped and right-clicked in the general vicinity of the monster. This would still attach those particles if the monster was "close enough" to your cursor when you clicked.