When you listen to, or play, a piece of music, you are probaby aware that there are many patterns. What do I mean by patterns? A pattern is a short musical "thought" or idea (sometimes called a motif) that often becomes the basis for that composition, or that section of the composition. It is a sequence of notes (and rhythm, of course) that our minds can grasp. The original idea or pattern is then repeated, altered, embellished, possibly transposed (moved to another key) in a myriad of ways. Yet however much it is altered, it is still recognizable as the pattern, as opposed to being new material. A short piece might actually only have one basic pattern; a longer one would need several to keep it from being too repetitive, and thus, predictable and boring.
When you look at a painting, you see all the relationships of the parts to the whole at one time. Music, on the other hand, unfolds over time, so it is much more challenging to hear the relationships of the parts to each other and to the whole. In fact, we hear in "retrospect;" what we hear at the current moment is compared with not only what came just before, but even several minutes before. It's pretty amazing when you think about it; our brains retain the themes that we previously heard, and can recognize them again, even when altered and embellished. If this weren't so, most music would be impossible to understand, and certainly to remember. It would just sound like one note after another, in an arbitrary way.
Pattern recognition is considered important in many fields. Some form of pattern recognition is a part of many aptitude tests.
I find a wide range of abilities in pattern recognition among my students. Some see/hear them right away, others do not and need to have them pointed out. I find that people in tech have a greater aptitude for pattern recognition than the general public, which makes sense.
However, there is a LOT more to the story for a musician. Many people studying the piano might be able to recognize the patterns looking at the notes on the page. However, getting those patterns out of your head and into your hands is a whole other matter. Applying pattern recognition to your physical technique in the right ways will help you learn the piece more quickly, execute it better from a technical standpoint, make it more musical, and memorize more easily.
Here's an example.
A student of mine was playing a Bouree by Bach. A Bouree is an old French dance, characterized by a short two- or three-note pattern which correspond to the steps in the dance. In the music, this short pattern can move up or down, can be inverted (turned upside down) and slightly altered in a few other ways. To convey this dance-like quality to the listener, the hand must play them all in basically the same way. If you just concern yourself with "finding the notes" you will likely get a mish-mash which will destroy the subtle phrasing of the dance, and you will possibly have a hard time learning to play it. I had the student block the notes of each group (see my post titled Blocking), and then move the whole hand up or down accordingly. It was important to use the same fingering for each repetition of the pattern! The fingerings marked in many scores are very convoluted, in my opinion, and do not follow the idea of having the hand do it the same way each time. Why learn several ways of playing a short group of notes when you can instead learn ONE way. After blocking it several times, he played it as written and it went much more smoothly -- and musically.
What I want to emphasize here is that intellectual pattern recognition is not enough. The execution of patterns must become a part of your technique. A good teacher should be able to help you with that.