Congress is referred to as the "legislative" branch because it makes laws, or legislation. It consists of two houses, a Senate in which residents of each state each have two Senators, regardless of population, and a House of Representatives, which is meant to have Representatives apportioned in a manner reflecting population.
A strength of this system is that it attempts to balance the interests of geographical regions with the notion that all voters should be equally represented. A weakness is that it is undemocratic in the sense that it dramatically violates the principle of one person/one vote. California, with over 37 million people, has precisely the same number of Senators as Wyoming with under 600,000, meaning that one voter in Wyoming has a much say in selecting a member of the Senate as 50 Californians, something that appears rather unfair. Due to the methods by which seats in the House are apportioned, the number of people represented by a member of the House can vary by some 400,000, meaning that some voters have the equivalent of twice the number of votes as others.
Due to the size and differences in composition between the Senate and the House, it can be difficult to pass legislation. In some ways, this is a good thing, as it makes the process more deliberative rather than simply responding to crises and changes of fashion. On the other hand, many needed sorts of legislation, such as those to upgrade crumbling infrastructure or reform an unwieldy tax code, may struggle to get passed.
Having direct Presidential elections rather than a parliamentary system can be a strength, as it gives a more direct voice to voters than having a prime minister who is simply the head of the winning parliamentary party, but it also can be a weakness in that the executive and legislative branches sometimes do not play well together.
The main strength of the legislative branch is that it has almost all of the legislative power in our country. That is, it is the branch that actually has the power to make laws. Of course, it is true that the president can veto laws that Congress passes. However, Congress can override his veto if it wishes. More importantly, the president cannot actually make any laws. When President Obama wanted to create the health insurance system that we now call “Obamacare,” he had to ask Congress to pass the law. He was not able to make it happen simply by saying he wanted it. Because only Congress can make laws, it is a very strong branch of government.
The major weakness of Congress is that it is so big. There are 535 voting members of Congress. Even the Senate, which is much smaller than the House of Representatives, has 100 members. This means that no individual member of Congress is very well-known to the general public. Because no members of Congress are really well-known, they cannot easily lead. If a member of Congress wants to propose a major change in policy, he or she will have a very hard time getting most Americans (or even other members of Congress) to pay attention. A member of Congress who tried to propose something really big (like Obamacare) would have a hard time persuading the public to support the proposal because no one would pay attention to them.
Congress is strong, then, because it has the power to make law. However, no individual member of Congress can typically exert much leadership on the national stage. Therefore, Congress is at least somewhat weak because it cannot usually lead the country.