Why do the negative and positive wires (directly from power source) spark when connected.Why doesn't that happen while it's connected to an appliance like a bulb?
When you manually let two wires touch, there will contact bouncing: there will be a quick sequence when the circuit is closed and when it is open. Now, one cannot break a current instantly when there is inductance (and there will always be some inductance in any circuit). This will create a voltage that is proportional to the rate of current change and the inductance. Can easily be high enough to induce sparks and arcing in air.
Also, such contacts will be covered with oxides and other crud, causing a contact resistance. A large current will give rapid heating, proportional to $I^2$. When a contact like that breaks, some metal is also likely pulled from the surface, microwires that will vaporize.
All these effects increase when the current is larger. It is a bit of an engineering problem to make high-current switches.
A way to think about a good conductor like a wire is that there is something like "electric pressure" in this world, which we call "voltage", and by letting electrons move so easily through it, a wire has the same pressure all throughout its volume. This is much like how most of the room you're in right now is at the same pressure and therefore there are no sudden gusts being created -- that is because the air is free to move throughout the room. Pressure pushes air around, voltage pushes charges around.
There are also things like fans that we call batteries: they have a very predictable pressure difference where one side is smaller than the other. Unlike fans which require a constant input of energy because they're losing energy constantly to friction, batteries tend to be based on chemical reactions which just slow down and stop when they see that "back-pressure", so they don't waste that energy all the time, just when there's a way for electrons to get from the one terminal to the other.
A spark is a different phase of matter called a "plasma", which is a little like a gas phase but also a little like a metallic phase: a plasma has to have these "free electrons" which are not sticking to the atoms but are moving between. One way to create a plasma, like the Sun does, is to just be so hot that there are always these random thermal "kicks" knocking electrons off of atoms. Another is like lightning does, to have such a big voltage gradient (change in voltage per unit distance) that it rips the electrons off the atoms. The same effect is also seen in static electricity: in this case you need one surface which is a little sticky for electrons, like plastic or rubber, and another substance where the electrons do not stick very well at all, like your hair. It's almost the same thing: the very light voltage gradient that is the "stickiness" of the surface is enough to rip apart the very loosely-bound atoms in the substance.
Anyway the "dielectric breakdown strength" of air is the formal term for what voltage gradient is needed to rip apart the electrons from the air atoms, and it is 3 million volts per meter. This means that if you have a 12 volt car battery and jumper cables attached to both sides, you will see a spark whenever the cables get as close as four micrometers -- this is small but it's not that small, it's maybe one tenth the thickness of my hair.
You may also see phenomena which are a little bigger than this tiny little bolt of lightning, often flying off in all directions, and you may call those "sparks." They are not quite the same thing. It turns out that every conductor is not 100% ideal and electrons moving through them generate heat, which causes a loss of electrical energy (causing the voltage to not be perfectly the same on both sides). The lightning spark is a much worse conductor than the jumper cables, so a lot of energy gets lost in this tiny bit of space, which makes that space very hot, often hot enough to melt and fling off little bits of metal. So in some ways that's not the "spark", since it's just hot flecks of metal flying in all directions: but since metal glows brightly when hot, it can kind of look like a spark does: tiny and bright.
The light bulb is actually a very tiny wire that glows brightly when hot, and is a worse conductor than the wires around it, so it gets very hot inside the bulb. When it is not connected to a battery the electrons usually just flow backwards through it, so it does what all conductors do and comes to the same voltage on both sides. That's why you don't see it spark the same way.
When the wires are connected, it forms a short circuit, with extremely high amounts of current flowing through the wire due to the negligible resistance of wires. This causes sparks. The bulb has non-negligible resistance, and since voltage is constant and V=IR, there is less current flowing through the wire, so there are no sparks.