Learning relies on memorisation. Learning a physical skill efficiently, such as riding a bike, requires a basic part of our brains to remember the important movements. When we first start learning to ride, we think through all the tasks, like keeping feet on pedals and pushing. After a while we just seem to be able to do it no thinking. Likewise, learning something we can recall and use, such as times tables or spelling words, takes deliberate rehearsal repeating, at first with the information written in front of us and then just from memory. Both types of learning take practice until we feel like we just know the answer or what to do. Piano playing relies on both types of learning physical and mental which is an important reason why we need to practice daily.
People who are good at memorising things like new names and faces or history dates often say that they practice how to memorise and recall things. They use tricks that work well for the different ways that they think. Some people make pictures in their minds, stories or patterns. Some people sing, repeat out loud or make rhymes and rhythms. Some people have to be active, like going for a walk, so they can think best. To remember things well, we each need to find a technique that works for us.
An interesting thing about playing the piano is that it uses all these different possibilities at once. Reading music and playing the piano involves sound (rhythm, melody, patterns and direction), movement (finger action, direction across the keys), visual images (piano key patterns, images and patterns on the music score) and has great scope for making stories. Each pianist has to work out the way they best memorise and learn well so they can make the best possible progress and learn pieces more quickly and fluently.
Why would we try to memorise music? For people with good aural skills it is pretty easy to tell, but the same thing applies to everyone memorising music makes playing the piano easier, and therefore more fun. What looks like a mass of confusing black dots on the paper can very quickly be turned into a few simple hand placements and easy finger actions. Once you know where your hands are supposed to be and where they are moving to, you can stop worrying about all this extra information and start listening to and enjoying the sound you make. Memorising makes piano playing easier and more fun.
Memorising is also vital for being able to play without stopping or hesitating. We need to be able to do this to perform a sensible piece of music instead of lots of pieces like a scrambled jig-saw puzzle. This is called reading ahead when we have the music score in front of us. Basically what we do is look at the music ahead of what we are playing. We know, by identifying patterns or shapes we have recognised during practice, what we will be playing before we have to play it. Recognising it means we are already to play it we dont have to stop to get ready. If we follow recognition with purposeful memorising, we learn even faster. Therefore, by actively using our memory when learning music, we can also play pieces that are far more complex than we are able to keep up with if we have to read everything. (A little secret here, this is how your teacher can tell if you have practiced properly how you have progressed in quickly recognising and preparing for what you need to do next.)
Some people find it easy to memorise and feel safe playing without the score. Some people need to have the visual reminders hidden in the score. The second group sometimes forget that they, too, are relying on memory. Both groups need to actively use their learning style to memorise well. Very few geniuses can memorise quickly a piece from beginning to end so lets start by keeping our learning tasks bite sized. Start out by getting small groups of notes into memory, small enough that you can LOOK / COVER / PLAY / CHECK just like spelling.
Now, music can be even easier than spelling because most of the notes and sounds are actually more related than spelling words. For example, you might have a starting note A and then 5 notes moving by step higher. All you need to remember is A and 4 more steps. Even easier, this might be thumb on A then every finger in a row. As you get more comfortable with different movements on the piano, moving up through higher levels, this principle still exists. Instead of thinking single notes you might need to think about chords, like I to V7 or an arpeggio, but often you will still find scales or little sequences like fingers 1 3 4 2 then 5. By playing groups of notes at once or building a block of notes and then breaking down the patterns into finger movements, memorising can be achieved much quickly and so can learning to play sections with speed.
So, make efforts to memorise all the demanding section of your pieces when you are practicing and you will be able to play the music with greater ease much sooner. (Remember to regularly check what you have learnt.)