I found this to be quite difficult to explain and some of this information goes beyond even first year university
Lets take a look at equilibrium. The reaction A + C ⇔ D + E. We can easily write the equilibrium constant as k = [D][E]/[A][C], but what exactly does k mean?
K is the ratio between two constants, known as rate constants. Rate constants are used like any other constant in physics. The rate of the forward reaction is (rate forward = Kf[A][C]) and the backwards (rate backward = Kr[D][E]). Kf and Kr are the rate constants (which I will show below how they are derived). As you can see the rate of reaction is proportional to the concentration of reactants multiplied by their rate constant.
At equilibrium the rate of the forward reaction must be the same as the backwards reaction. This means that Kf[A][C] = Kr[D][E]. We can rearrange the equation to be Kf/Kr = [D][E]/[A][C]. Now, Kf/Kr is also a constant (a constant divided by a constant is constant), we can write it as Keq, which we know as the equilibrium constant.
How is the rate constant derived? There is an important equation, called the Arrhenius equation (attached). It shows that the rate constant is related to A (collision factor, it is related to the proportion of collisions where molecules collide with the correct orientation), activation energy and temperature. The collision factor, A, is related to temperature, and also temperature is a variable in the equation.
When you change temperature, some of the values in the Arrhenius equation change. However, the amounts that Kf and Kb change differ (not by the same factor) and the ratio between them also changes. This can be seen when the temperature is increased. The endothermic reaction will be more favored, because the rate constant for it increases in a higher amount compared to the exothermic reaction.
Pressure has no effect on the values of the rate constants. The reason that pressure effects a system when there is a difference in the amount of gases in the equation (e.g. A(g) <=> C(g) + D(g)) is because the rate of forward and backward reaction don't change by the same proportion. Rate of forward = Kf[A] and Rate of Backward = Kr[C][D]. If you double the concentrations (by doubling pressure), the forward reaction will increase by 2x and the backwards reaction will increase by 4x, because Kf[2A] = 2x Kf[A] and Kr[2C][2D] = 4x Kr[C][D].