The Tier system is a progression-based rank which increases (or decreases) based on population size. Clicking on the "Population" box will bring up an overlay which has a button called "Set Growth". This allows a user to manually set the population growth (eg: maximum) or set it to automatic. The system will determine the growth rate based on how much extra food you produce compared to how much your nation uses.
Tiers also determine who you can and can not attack. You will only be able to attack a nation if they are the same Tier as you. However, it should be noted if you are Tier 6 and start a war then rank up to Tier 7 you will still be able to deploy more units until the war is over.
You can set your population to stagnate (neither increase or decrease) by setting a custom growth of 0. This allows you to stop just before the next Tier and stockpile resources, increase production or train your military.
Population requirements: 0-74,999 (population cannot go below 40,000)
You will not be able to do much at Tier 1 other than the basics of building resource factories and growing your economy. Food is the key element at this stage as it will allow you to increase population growth and tax income. Tier 1 is really just meant to give you time to get familiar with the interface and general mechanics.
Population requirements: 75,000-249,999
During Tier 2 you will be introduced to a few more options and challenges. Population growth requires urban areas (which are taken from cleared land) This means you will need to keep an eye on how much spare land you have and how much you can produce (you can clear forests, mountains etc to produce cleared land). You will also be introduced to the requirement for Consumer Goods at 100,000 people. Power is another important aspect that will be introduced here because urban areas consume power. You will have to manage your power supply to both your factories and your urban areas.
Population requirements: 250,000-599,999
Tier 3 is when you should start to think about an organized military with multiple divisions and begin to train them by sending them on missions. You should be familiar with the basic mechanics at this point and can get started on understanding the more advanced options such as building upgrades, factory upgrades, importing and exporting resources and resource discovery.
Population requirements: 600,000-1,199,999
Tier 4 is where players are now deemed sufficiently versed in the game mechanics to the point that more advanced economic progress can be made. Although it is down to player preference this is a great tier to start stocking up on raw resources (cows, sheep, iron etc) through resource discovery. Joining an alliance is also a good idea as you may become a target when you reach Tier 5. Another bonus about being Tier 4 is that you can build an equipment crafting building. Equipment Crafting Buildings allow you to (obviously) craft equipment.
Population requirements: 1,200,000-1,999,999
The main bonus for Tier 5 is the ability to gain hops to construct breweries. Breweries are the most efficient Consumer Goods factory in the game (at base level). Another bonus is being able to buy Colonists. The Colonists item is basically like Expand Borders, except a lot more expensive, and instead of expanding your borders on your home continent, you can choose another continent to colonize. These should be mainly bought when on a big sale
Population requirements: 2,000,000-3,499,999
Tier 6 is an exciting time if you have a large military and a large stockpile of fuel and ammo. You can use these resources to get fighter planes.
Population requirements: 3,500,000-5,999,999
Tier 7 is when you want to be focusing on the sustainability of central production. Ex: Moving away from consumable factories (Dairy, Coal Power Plants, etc.) for goods such as food and power. Now you should try building more factories such as windmills, farms, hydro-plants, etc. that do not require any discoverable resources (cows, coal, etc.) to function.
Population requirements: 6,000,000-17,999,999
Tier 8 is when you have most of the available buildings built and upgraded and are seeing higher and higher population requirements. By this point, you should be trying to increase the efficiency of your sustainable factories to meet the increasing demand from your growing nation. This is done by going to your factories, and clicking on the three vertical bubbles on the bottom-right of the card.
Population requirements: 18,000,000-69,999,999
Tier 9 requires players to grow their population by 388% to get to Tier 10. Navigating the complexities of this Tier can not be fully explained in a short section and it is recommended that you get active on the forums and discuss ideas/suggestions with other players.
Population requirement: 70,000,000
At this point, you have stopped growing population wise and should be growing in other ways. These could be in production, military, natural resources, etc. But because you have stopped growing, the amount of money you get from population and taxes stagnates, so be wary of expanding too much.