How to even begin answering this: I once wrote in my private writings, If liberty was God's gift to America in the 18th century, Abraham Lincoln was the gift He gave to America in the 19th Century. I have a hard time overestimating his importance, because literally everything he did was so perfectly timed, so meaningful, and so effective that even his political enemies often marveled or became his friends and allies.
1. He was extremely selfless and quick to forgive. Most of Lincoln's cabinet was made up his rivals from the 1860 Republican Convention. In previous administrations, Presidents filled their cabinets with cronies or spineless ciphers. Seward, Chase, Bates, and Blair were all very capable men and were all very good at their cabinet positions. When Lincoln made changes, they were filled by capable men, most notably Edwin M. Stanton as Secretary of War. Lincoln also gave several men multiple chances to succeed or fail, such as General McClellan.
2. Lincoln knew the art of taking the blame when it best suited. When many were calling for Stanton to resign, Lincoln made a speech not only protecting Stanton, but personally taking the blame for the failures that Stanton's critics were trying to use against the Secretary of War. By taking the blame himself, he protected Stanton (whom he needed desperately as secretary of war), he built trust and confidence with Stanton (and, by extension, the rest of the cabinet), silenced Stanton's enemies, and diverted the blame to a place where his enemies couldn't touch (himself, elected president and was more or less untouchable there until the end of the term). Lincoln knew that blaming his predecessor was political suicide.
3. Lincoln was an excellent judge of character. He was able to judge people's motives better than they themselves, and was able to rise above that, able to make proper decisions in spite of it. Secretary of Treasury Chase was never a loyal member of the cabinet: even as secretary he was using his influence to undermine Lincoln's chances at getting renominated in 1864. Knowing Chase's political treachery, he kept Chase on for months, as he was supremely capable of financing the war. Only mid-1864, long after much of the heavy-lifting was over, did Lincoln finally accept Chase's fourth resignation letter, much to Chase's surprise.
4. Lincoln didn't worry about side issues. When General Grant was facing General Lee, he sent back massive numbers of dead and wounded, and some were calling Grant a butcher. Even Mary Lincoln criticized Grant's losses of men. Lincoln refused to caught up in the details (we have to call the deaths of thousands of soldiers details, sadly), and recognized Grant's talents of defeating his enemies.
5. Lincoln, better than any other President, was an excellent judge of his constituents. Consider this, in 1861, Maryland was on the cusp of secession; they tore up rails and cut telegraph lines, endangering Washington, but in 1864, Maryland ratified a new state constitution, outlawing slavery. Had Lincoln tried to end slavery in 1861, Maryland, Missouri, Kentucky, and Delaware would all have seceded; but by the end of 1862, the country was ready for the Emancipation Proclamation, black soldiers, and a change in the nature of the war. By the end of the war, Maryland was the fourth state to ratify the 13th Amendment ending slavery. The timing was perfect.
There's a reason Lincoln has more biographies than any other President: he was successful when many of his opponents would have failed, he led when many others were afraid to step out, and he could read people extremely well. His reputation as a great President is well-earned, and all have much to learn from this western lawyer from Illinois.More questions on Abraham Lincoln: