Space Travel: From levels 1-5 your fleet is rather small (no more than 8 light ships) and unable to do FTL travel without using a Travel Gate, and they are rare and expensive to use. From levels 6-10 your fleet can include some heavier ship and be able do FTL travel without a Travel Gate, although it is unreliable. From levels 11-15 you have a small fleet with some heavy ships and FTL travel is now reliable. Higher level gets you even more ships. You can have less ships and give the ones you have more advanced systems.
Weapons: Levels 1-5 grant you above average modern firearms and some understanding of laser technology as weapons. Levels 6-10 allow you to have laser weapons as standard, although they have short range, or have more developped solid projectile firearms. Levels 11-15 give understanding of gauss technology as reliable weapons and plasma weapons as an option (not the most reliable one, but it is still an option). Higher levels give more tech that you still don't know.
Armor: Levels 1-5 give above average modern body armor and the first laser-proof armors. Levels 6-10 allow you to start having primitive force fields and power armour. Levels 11-15 grant more sophisticated force fields and even mecha armour. Higher level=more tech you have to discover.
Genetic Engineering: You'll have to be the ones asking what you want, and i'll tell how much it is, because this is a broad subject.
Numbers: Levels 1-5 are about platoons, and you get to around 400 men. Levels 6-10 are an army, with numbers getting close to the thousands. Levels 11-15 are big armies, and you have thousands of men. Higher levels, higher numbers.
Discipline: Levels 1-5 are armies with an above average discipline. Levels 6-10 means that your men have usually rites of passage and other traditions that make them be a different society on their own. Levels 11-15 usually haver some kind of religious conviction that their orders are right and good.
Support: Levels 1-5 give you an ally that has some interest in your field and wants to take advantage of the results, so it helps you to get to them. Levels 6-10 are about allies that have a long story of partnership and will support each other almost all the time. Levels 11-15 are more like a brotherhood than simple allies.
Vehicles: Levels 1-5 give you access to standard military vehicles. Levels 6-10 allow you to take more sophisticated vehicles like fully sealed tanks that can be use in planets with a corrosive atmosphere. Levels 11-15 are true killing machines and leviathans, like an Imperial AT-AT (Star Wars) or a light Scout Titan (WH40k)
Psychic Levels 1-5 mean that at least 5% of your soldiers have useful powers. Levels 6-10 give you higher percentages and more powerful pshychic powers, like telephatic communication between continents. Levels 11-15 are all-psychic users with most of them having serious powers.
EDIT: Maybe the numbers may seem low for those of you that want a higher number of men, but remember that your project started no so long ago, and the Goverment has lots of projects like this. At first you'll be a bit low on funds. When you have decided, I'll start an IC thread with the details for your first mission. Remember, you can always ignore the missions and look after your own goals, but the funds come from the Goverment, and the Goverment wants results.