I assume you mean amendments other than the original ten, as they were passed shortly after the adoption of the Constitution. It is impossible to create a laundry list of each amendment; but a few notable examples are in order:
The thirteenth, fourteenth and fifteenth amendments were passed at the time of the civil war. They were designed to end slavery, guarantee citizenship and equal rights to the freed slaves, and guarantee that they had the right to vote. As originally drafted, the Constitution was silent on the issue of slavery, although its language led most scholars to believe that it was constitutionally protected. For that reason, a constitutional amendment was needed to end it. By the same token a constitutional amendment was needed to protect freed slaves.
The Sixteenth Amendment provides for an Income Tax that need not be apportioned among the several states as provided in the original constitution. The Seventeenth provides for direct election of Senators; and the Eighteenth was the "prohibition" amendment. These were all part of the Progressive movement of the late nineteenth and early twentieth century in which it was believed that the cure for the ills of democracy was more democracy. The eighteenth was repealed by the 21st Amendment which had proved unworkable.
The twentieth amendment changed the dates for Presidential inaugurations. With new methods of tabulating and reporting votes, the long wait which had hitherto existed were no longer necessary; plus the long "interregnum of despair" between Franklin Roosevelt's election and inauguration indicated that a long lame duck term was not good.
The twenty second amendment limited the President to two terms. This was after Roosevelt had been elected to four terms; and it was generally agreed this had been a mistake. Roosevelt had been very ill by his fourth term and in fact died in office. He made concessions at the Yalta Conference which a stronger, healthier president might not have made.
The twenty fourth amendment outlawed poll taxes, a device used in many Southern states to disenfranchise black voters. It was part of the growing civil rights movement of the time. Finally, the twenty fifth, which provides for Presidential disability and succession, including the power of the President to name a new Vice President, was passed after the death of John F. Kennedy. He was succeeded by Lyndon Johnson who had previously suffered a serious heart attack. If Johnson had died in office, the next in line to the Presidency would have been Strom Thurmond, president pro tem of the Senate who was also up in age, and then the Speaker of the House who also was elderly. It was felt that a more orderly succession needed to be provided for.