What is Metagame? When I worked at Digital Chocolate we used to call it the place in the game where you place the ready buildings into the city. So, the basic gameplay would give you a building and in the "city mode" / metagame, you would place this building to the city. This would give you a purpose to make those buildings.
Metagame can be one of the most vital parts in your game! Without players will not find purpose to continue with your game and quit.
Metagame provides answer to the WHY question player has in mind. It gives reason to continue and at best it provides a goal why to continue your game for months if not years.
A metagame can be about building a city, conquering the world, filling your restaurant with tables, customers and orders, collecting all possible items and coins, evolving your character.
Usually it's game on top of the basic gameplay extending the purpose of playing your game.
Here's a sample of basic gameplay extended with metagame from Tower Bloxx.
The basic gameplay is about piling up blocks into buildings. When the level is over, the result is a building you can place into the city you build.
The metagame for our City Building Tetris would be building of the city.
First we give a meaning for every level. Playing a level produces a house. The amount of floor the house has is the amount of rows you managed to complete and remove.
Second, you place the house you got from the level to the city. Your goal is to fill the city with the houses. To make it more complex, each level could provide a theme for the house: residential, commerce, industry, infrastructure like hospital, police and so, and it would be up to you to create enough the right kind of buildings.
After a while you might find yourself playing the game to manage a single level, but also to complete your city - that might even become your primary goal!
We could also have achievements, create a 30 floor high building, play for 20 hours. A trophy room, which we could call "City Hall Rewards" would show these achievements in addition to leaderboards, rankings, level rating, collectables that would appear on levels and many more reasons we could add to give you reasons to play the game longer.