I think most of you know, that in the written music score, two notes that are the same that are connected by a curved line is called a tie. That curved line connecting those notes means that you play those two notes as one note, holding it for the timed value of the two notes.
But many of you may not know that a curved line [called slur] connecting two notes that are not the same, means that you play the two separate notes connected in a legato like fashion, and it also means the second note is to be played softer than the first, resulting in a loud-soft sound.

In piano, this technique is called drop-lift. When a pianist sees two different notes connected by a curved line, it means he/she will drop down on the first note and lift up in a rolling fashion on the second note [with the result that the second note will be played much softer than the first note].
When you have a curved line [slur line] over many different notes it means you play those notes in a legato technique-by holding one note and not releasing that note until you begin to play the second note; but when there are only two different notes connected by a slur line you must also not just play them legato but also use the drop lift technique to play the second note softer than the first.
This technique is many times written at the end of a phrase in a classical music piece. You may not think this means much, but this technique really adds to the beauty of the piece. Along with rubato and ornaments [such as trills, and turns], the drop-lift technique [as it is called for the piano] helps make classical music sound beautiful.
That contrasting dynamic sound between two notes is really pleasing to the ear. Sometimes the contrast is subtle and sometimes it is pronounced.
UPDATE: I have been informed from Jim Denton, who was a cellist for many years for the Houston Symphony Orchestra [before his recent retirement], that I need to make a correction: “The second note of two slurred notes is not always softer, regardless of whether it’s a pianist playing them or a different instrumentalist. Those slurred notes my be located somewhere in the phrase where a crescendo is called for, either because it is “felt” or outright written in the music underneath the staff, due to what comes both before those notes as well as what comes afterward.”
Now let’s see if you can spot when the pianist uses this drop-lift technique. I will give two examples where the drop-lift of the pianist occurs.
In the first example I have the beautiful and dramatic first movement of Beethoven’s piano concerto #3. See if you notice the drop-lift technique used by the pianist at 4:19 – 4:20. I will let you see if you can find any more. Sometimes you don’t even have to watch the pianist, you can close your eyes and listen to the sound of the second note of a slurred two note combination being softer.
L.V. Beethoven: Piano Concerto #3 in c minor, movement 1, Allegro con Brio:
I will not give you any hints this time. Let’s see if you notice the drop lift technique in the beautiful second movement of Mendelssohn’s first piano concerto in g minor.
Felix Mendelssohn: Piano Concerto #1 in g minor, Movement 2, Andante: