Game goals
The games differ by the goal, which you should reach. You usually need to clean the level, but in some games there are other goals. Read this article to find out which game is the best for you.
Clearing the blockers
The most common goal of the game is to get rid of some blocks, which are on the screen. These are usually tiles, which you can see under every jewel.
Collecting jewels and items
In some games it is not sufficient just to clear the level. You also have to collect a number of jewels of certain colors in order to complete the level. An example of such game is Fruit Dash, in which you collect fruits, leafs and other items.
Reaching high score
Sometimes, the goal is just to reach certain score. You can see this however mostly in older games, like Bejeweled.
Time limit and moves limit
The goals above would be pretty easy to complete, if you had unlimited time and number of moves. The game would however get boring soon. There would be no challenge. This is why the games want you to complete the goal in given time or number of moves.
You can usually find your time/moves left at the top of the screen. An example of a nice timed game is Jewels. A good game, in which almost all levels are on number of moves, is Fruit Dash