There is a debate about "academics" verses "play" in preschool years. Basically an academic program focuses on teaching children primarily reading skills, and math skills by giving them worksheets, and assignments. The children learn rote memorization and can often regurgitate facts back to the teacher or parent. An example would be to be able to count to 100. You can certainly teach a preschooler to count to 100, but the understanding of the concept of "what is 100?" may not be there. In a "play" preschool, the children are learning all of the time, they are just constructing their own knowledge and learning it through concrete means. A child learning to count will count objects, or stairs as they go up or down. Numbers themselves are an abstract concept, children develop into abstract thinkers by experiences.
Here are some ways play dough is used to teach the needed concepts:
You may just see a child squeezing play dough, and rolling it or cutting out shapes with a cookie cutter. Some of the things I see are:
Fine motor development, the small muscles of the hands need to be worked to develop properly, this aids holding a pencil or cutting with scissors later. Being able to use a rolling pin to flatten the dough works the fine motor muscles and the larger muscles in the arms. Sometimes the dough is harder and takes more pressure, having to learn how much pressure to apply without making it too flat.
Spatial relations: making the dough the right size to fit the cookie cutter, children usually start out making it too small, part of the cookie cutter hangs off the edges. Later they are able to judge the size easily.
Math concepts including addition and subtraction: how to divide the play dough evenly for everyone at the table. How many pieces do we need, real life counting. There are four children, plus one teacher, how many pieces is that. Also math skills such as adding and subtracting, start with two balls of play dough, make one more, how many do we have now. Add another, how many now? Lets take away two, how many now?
Measurement/Size comparison: Children compare sizes of play dough balls, which is bigger, smaller, put them in order from smallest to largest, which is longer, how long is it, use a ruler, or a block to measure it. How many balls can we make, let's count them, then they are learning to count real, concrete objects, and understand what 1 or 20 or 100 means. They can learn one-one correspondence, meaning that they understand that when I point to one object I say "one". They also can begin to understand object permanence, for example, if I put out five objects and we count them, and then I add one more, developmentally, children will have to count the original five objects again, and then count the added one; but as they gain understanding they will start at five and count from there. Another example is that if I take a piece of play dough and break the same piece of play dough into two pieces, younger children will say I now have more play dough. They have to develop the understanding through concrete objects to understand that it is the same amount of play dough.
Social Skills: what to do to divide up one large clump of play dough into enough for everyone at the table, evenly. Then when another child comes, being able to share the dough a little more. Sharing the tools, sometimes sharing ideas about what to do with the play dough, what to create, making a group project. Joining a group is often hard for children. The social skills needed to join play is hard, but play dough is something that is easy to join. It makes that social transition easier. Then often those same children will feel comfortable playing at another activity together later, or will leave play dough and go to something else together. Play dough is great for solitary play, parallel play, or social play. They children can play at their level and feel part of the play.
Alphabet/shape The teachers put out a variety of materials to use with the play dough. When the alphabet letters are put out, the children can use them in variety of ways. They may just use them as a cookie cutter, or may use the letters to make the alphabet or their name. Letters are also made out of rolled play dough. The same types of things are done with shape cutters. Children at this age are concrete learners, they must touch to learn. Things have to be in solid form in front of them for them to understand it, they are not little adults who think in abstract ways. That is a developmental process that takes many years. When children are able to manipulate play dough into letters, it helps them form those letters with a pencil to write their names, it helps them to remember those letters when they see them written (which is abstract).
Listening to directions/conversation with teacher: Sometimes at the play dough table the teacher will give directions, make a small ball, make a rope this long, etc. This gives children the skills needed of listening, following directions, two step directions, and more. The children also have the opportunity to talk in important casual conversation with a teacher at the play dough table. They can discuss their pet, or what they did this weekend, and have a relaxed opportunity to talk. Conversational skills are something which develops, they learn the give and take of conversation, another child may join the group and they learn how to include them in the conversation.
Sensory experience: sometimes the play dough is warm, sometimes it is cold, it may be hard or soft, it may be a different recipe, it may have cinnamon in it or peppermint oil. The color changes and sometimes two colors are there to mix. Play dough is a wonderful, sensory substance which also helps children who are unsure about being in school to feel ok. When a child is upset coming to school, or is having problems separating from mom or dad, play dough is one of the best tools to help them feel ok. When they start squeezing it and manipulating it, they become so involved that school is ok. It is also a quiet activity, and feels safe. It can be a solo activity if needed, or others can be involved too.
I hope from this glimpse at how "playing" with play dough helps children learn the concepts needed for current and later school success, you have a better understanding that "learning and academics" are going on all the time in a good preschool setting. The materials are chosen with specific goals in mind, and the ways children play with them is teaching them. The most important part to understand is that children learn different than adults. They must have concrete objects to manipulate to learn. The more experiences they have, the more the brain develops.