Before sitting for meditation I got a few strange questions: why does my mind even wander? What does my mind want, and can it ever be satisfied completely? Can anybody please explain this to me?
Every life form is born in the world due to craving. Within life forms, there are seeds, such as sperm cells, which are propelled by craving. Parents of children engage in sexual intercourse & reproduce new life propelled by craving. New born children are born with craving to eat, craving to be safe, craving for love, craving for pleasure, etc. The mind wanders due to craving. This 'wandering' is called 'samsara'.
You ask as to why the mind wanders. But it is there for cognizing thoughts – just as the eye is there to seeing forms, ear for hearing sounds, nose for smelling odours, tongue for tasting flavours, and body for touching tangibles. That is why, the more we watch our mind and see what it does to us and for us, the more we will be inclined to take good care of it and treat it with respect. One of the biggest mistakes we can make is taking the mind for granted. The mind has the capacity to create good and also evil for us, and only when we are able to remain even-minded no matter what conditions arise, can we say that we have gained a little control. Until then we are out of control and our thoughts are our master.
Taming this monkey is not an easy thing. So you have to take baby steps in the beginning. Even if your attempt at meditation takes only a few seconds, or a couple of minutes, be happy about it. Left alone the mind behaves like a monkey in a forest. Meditation is a great way to calm the monkey mind. But prior to that we have to learn how to go beyond - being resolved on sensual passion, being resolved on ill will, being resolved on harmfulness—because all these things stir up the mind and interfere with its settling down.
why does my mind even wander?
Whenever there is a contact we perceive this as favorably or unfavorably, this results in a feeling of pleasantness or unpleasantness, this leads to thoughts of memories of the past or future expectations, these thoughts proliferate into more thoughts.
What does my mind want,
You mind always crave for sensations / feelings.
... and can it ever be satisfied completely?
Not by means of seeking pleasant experiences.
But still it it can be stratified if you practice meditation and realise Nirvana.
It's because of entropy, a natural law of nature which measures disorder (the higher the entropy, the greater the disorder), as physicist Rudolf Clausius stated: "The entropy of the universe tends to a maximum". The mind, like all conditioned phenomena, always tends toward scattering, fading away, disorder, decay, and cessation. It'd take effort to control and steady the mind just like proper effort is required to maintain a physical building from disorder and decay.