One of the great things I've noticed about Brahms is that, rather than trying to be dazzlingly showy or fantastically virtuosic, he seems to focus primarily on composing something that is simply a piece of musical and aesthetic excellence. The other Romantics were very focused on expressing human emotion at a more extreme level than previous composers, or portraying glorious imagery in their music; it was overall a very vivid, emotional, poetic kind of mentality that prevailed amongst the Romantics. Brahms, however, was what I like to call "the most Baroque of the Romantics," meaning that he, though a true Romantic, also seems to have preserved in his music the Baroque focus on "absolute music," music whose value is firstly in itself simply as music, in contrast to having value in the excellence of its portrayal of some external reality. The Baroque composers, especially those like J.S. Bach, were generally masters of "absolute music," whereas the Romantics maximized the idea of "program music." Brahms, however, being perhaps one of the greatest fans of Bach who ever lived, seems to have been strongly influenced by the latter's musical worldview of "absolute music." Brahms seems to have been very concerned with simply making music which was excellent just as music. This isn't to say that there is no poetry to his music; there is. He is both a Baroque and a Romantic composer simultaneously, which is why I love his music so much. His music partakes in the best of both worlds: the high intellectual mentality of the Baroque, on the one hand, and the poetic, imaginative, emotional drive of the Romantic, on the other. The complete formation of the human soul involves a deepening of the rational powers as well as the sensible powers, the emotions and passions. This is why Brahms is so amazing to me.
Anyway. Enough of my rambling. The best way to understand Brahms or any other composer is by listening to the music. So here it is: Brahms' Piano Concerto No. 2, as performed by the famed pianist Maurizio Pollini. Enjoy.