New land become unlocked when you prove that you can handle adding another area to your territory. This will involve paying a certain amount of points and reaching a specific milestone in the new area in a set amount of time. If you are successful you will permanently unlock the area but if you fail to meet the milestone you will not unlock the area and you will lose all the buildings that you constructed on it and will have to pay to try again.
In order to help avoid wasting your resources there are several things you can do before you start using them on trying to unlock the new area. Most importantly you need to make sure that the rest of your city is ready to support it so look to build roads and houses near the land you want to unlock as the new area will need to rely heavily on the income from those residents. Also ensure you have enough money to support development in the new area so you are able to construct new roads and other structures and check that your population is not maxed out. If you find it is don't attempt to unlock the new area until you rank up.
Once you initiate the unlock you will be given a random challenge you need to achieve. This could be anything from collecting a certain amount of coins to gathering specific items. If you fail in reaching your milestone the game will allow you to extend your deadline for a month. You will be able to keep extending your deadline for up to five months.