Samyama means perfection concentration or perfect control. So you are not far off that samyama is concentrating on something, and depending on which object you concentrate on certain siddhis can be awakened. However, this is not concentration as we normally understand it, like straining to focus on something. This conjours up images of people straining really hard to try and move a pen using telekenisis and giving themselves a headache lol On the contrary, it is more like a sustained meditation.
A sustained meditation differs from concentration because while concentration involves effort to focus on something, meditation does not require effort but only the discipline that as soon as your mind starts to wander from your object, you will notice it and then bring it back. You will maintain this process indefinitely and if your meditation is successful, you will start to shift into more deeper states of consciousness. If you continue to maintain the process, you will shift into even more deeper stages known as samadhi. It is at these stages that the siddhis associated with your object will start to manifest.
In order to understand why this is possible I will explain briefly the theory of Samkhya behind Yoga. According to Samkhya all matter exists at several level ranging from gross physical matter to the most subtle mental matter, to the absolute subtlest matter which is the three fundamental forces of the gunas. This most absolute level is known as the moolaprakriti field, meaning quantum or fundamental/root level of matter. In Yogic Samadhi one is accessing this level of reality of the object they are meditating on. This is why one is able to gain access and control of the root level of matter Some siddhis will become available at lower levels, like for example being able to control your heartbeat and body temperature, but most of the Siddhis patanjajali describes can only become available at the higher levels.
Now Patanjali warns that siddhis are not the goal of Yoga, they are more of a biproduct of the process and also a signpost that you are on the right track. So try not to meditate waiting for a siddhis to appear or meditate to attain a certain siddhi. Simply do your meditation and the siddhis will start to naturally come based on your progress.
I will add: Patanjali describes samyama as a combination of dharana, dhayana and samadhi. This basically means that as soon as you have selected your object of meditation in the dharana stage, it will naturally lead onto the dhyana and then to samadhi, and then depending on which object you selected, the siddhis linked with it will activate. For example, if your object of meditation is the Udana Vayu in your body, the upwards pranic current. Then you will meditate on this, this will progress through the dhyana stage to the samadhi stage, and you will attain samyama on the Udana vayu and the siddhi of levitation and flying linked with it.