Synaptic Plasticity literally means the ability of the connection between two nerves to strengthen when learning something or weaken when forgetting something. I know, that may sound funny but it is very important to be able to forget as well as remember.
The end of the nerve has a bouton which is like a little pod. In that pod are little containers of chemicals called neurotransmittors. When an electical charge comes down the nerve, the containers of neurotransmittors are moved to the edge and they release their chemicals into the space between the two nerves. At this point, the chemicals attach themselves to receptors on the next nerve and open a tube that allows calcium, for example to rush into the nerve changing the charge sending the electrical charge down the second nerve. In other words, the way a nerve works is first there is an electrical charge which turns into a chemical change and back into electrical charge in the connecting second nerve.
Here are a few pictures:
Here is a short animation of the synapse and how it works:
Now, back to synaptic plasticity and Down syndrome. The ability of the synapse to adapt and learn is dependent on BDNF (Brain Derived Neurotophic Factor). Oh no, more letters!!
This chemical (BDNF) is a necessary part of learning. When the amount of DYRK1A was decreased, BDNF increased and so did synaptic plasticity. So having 1.5 times of DYRK1A as much as normal, decreases the ability of the synapse to change and therefore, learn.