Why do things move? I mean, really, why do things even move? Despite the concepts of forces or mass, why does an object move? What is movement?
Even in the smallest scales if you think, let's say a plank length, anything that moves within a certain time, there will be a really tiny fraction of time where the object will eventually move 1 plank length. So, within that tiny moment, that object would have to kind of teleport to move 1 plank length because anything that exists within that length wouldn't make any sense, according to the theory at least, although this plank length and teleportation thing is completely my idea and I don't know for sure if they can explain why things move, but I'm really baffled by this phenomena! I've thought deeply, but I can't figure out its actual cause. Is it something that Physics has yet to explain?
I hope you've understood my question, please don't send any negative feedback. Thank you.
 A: 
What is movement?

In classical point particle mechanics let us take an inertial reference frame and an apparatus that allows us to measure the time (whatever that means). Let us also take a test point particle of inertial mass $m$. When the clock is at, say, $t_0$ we measure the position of the point particle with a ruler; say that is $x_0$. We repeat the experiment at $t_1\neq t_0$ and measure $x_1$. Once so, we calculate
$$
\bar{v} = \frac{x_1(t_1)-x_0(t_0)}{t_1-t_0}.
$$
If the above is different from zero then we say the point particles has been in motion during the time interval $t_1-t_0$. Otherwise we say the particle to have been at rest.

why do things even move?

It is an experimental fact that for some reasons, in the universe, there exist interactions among point particles such that, when subject to such interactions the particles change their initial state of motion in the direction of the external interaction (to be more precise, of the resultant of all external interactions). To why experimental facts are so, it is not a question that concerns physics (which is instead the science of how things happen, not why - see Feynman on why questions).
In quantum mechanics and quantum field theory the ideas tend to get more complicated, as it is unfeasible to actually measure with a ruler what happens at $x_1(t_1), x_0(t_0)$. In those cases physicists use the terminology of evolution of a system, namely whatever the quantities we can measure are, if those quantities change against time then the system "has moved" (has evolved). States of systems are represented by (equivalence classes of) elements in Hilbert spaces of any other similarly complicated object that obeys some particular equations of motion more or less complicated. The idea is nevertheless always the same, namely to compare the same quantities in different evolution times of the system. And again, to why it happens to be so, more than saying that it is an experimental fact physics will not help very much on that.
