If the Big Bang theory is true, what caused it to explode? According to the Big Bang theory, all the matter in the universe was amassed together at one single point. If this was the case, why was it able to explode? The density of the mass would create a tremendous gravitational pull, stopping any explosion from happening. 
 A: The Big bang cosmological model is based 1) on general relativity and 2) on quantum mechanics. Using known particle and nuclear physics processes the history of the universe is built up as seen below.

General relativity has solutions with singularities which are both attractive, as in black holes, and "explosive" as in the first Big Bang model. In GR energy is not a conserved quantity in general, so it can be postulated out of nothing.
The beginning of time  is in the present model above modified with the quantum mechanical fuzzines seen in the plot. Quantum mechanics also contributes to the inflation period, where the inflaton field homogenizes the energy soup. After that, known particle physics and then nuclear physics are used to model the history of the universe as we observe it now.

According to the Big Bang theory, all the matter in the universe was amassed together at one single point.

So it is not one point at the present standard BB model, it is a fuzzy region in the beginning of time.

If this was the case, why was it able to explode?

For the same reason that a bomb explodes: the cohesive gravitational forces are very  much smaller than the kinetic energy of the broken parts. In the case of the big bang the radiation motion of various quantum mechanical entities is very much stronger than the attractive gravitational interaction of these entities to each other.
The original explosion is allowed by the mathematics of general relativity, as stated above, there are many types of singularities in GR. In the present model  the quantum mechanical nature contributions fit and thus explain the observations as seen in the cosmic microwave background data.

The density of the mass would create a tremendous gravitational pull, stopping any explosion from happening. 

At the beginning it is an energy soup, it is not mass but a lot of radiations with quantum mechanical entities.
