What exactly is "voltage drop" across a circuit element? what exactly is "voltage drop" across a circuit element? I don't quite understand what this means. 
 A: If you have a simple circuit with resistors, the voltage at the source decreases throughout the circuit. At the positive terminal of a battery for example, you might have a voltage of 9 V, while the negative terminal can be taken as the ground potential 0V.
The voltage in between those terminals (that means through the circuit) decreases from the positive voltage 9V to the ground potential 0 V.
How does it decrease? We assume that we have perfect conductors as wires, which means that they have the same potential at every point, i.e. at the beginning and the end of the wire, the voltage is equal. The only points in a circuit where the voltage can decrease are the resistors in that case. In front of the resistor is a higher voltage, and behind it a lower voltage. The difference is the voltage drop. It corresponds to the amount of power dissipated in the resistor and is proportional to the resistance.

Here is the schematic of a simple circuit. As you can see, there are three resistors in series and a voltage source of 9 V.
A current of $0.5 mA$ flows through the circuit, and it flows through all circuit elements. We can calculate this current by finding the equivalent resistance of the circuit. For a series connection of three resistors, we just add their resistances:
$$R = R_1 + R_2 + R_3 = 3 k\Omega + 10 k\Omega + 5 k\Omega = 18 k\Omega$$
From $U = R I$ we can find the current flowing through every element:
$$I = \frac{U}{R} = \frac{9 V}{18 k\Omega} = 0.5 mA$$
Now we can find how much voltage drops at every element. It is proportional to its resistance. Since we now know the current and the resistance at each element, we can calculate the voltage drop.
For the voltage that falls off at $R_1$, we write: $$\Delta U_1 = R_1 I = 3 k\Omega \cdot 0.5 mA = 1.5 V$$
Similarly for the other resistors we get $5 V$ for $R_2$ and $2.5 V$ for $R_3$.
In the circuit above we can see how this changes the voltage levels at each part of the circuit. Coming from the positive terminal of the voltage source, the voltage is 9 V. It stays this until it reaches the first resistor. At the front of the resistors (in direction of the current, clockwise), the voltage is 9 V (the red part), but the voltage behind the resistor is lower: it is now only $9 V - 1.5 V = 7.5 V$ (the yellow part). The voltage dropped over the resistor. If you'd probe the voltage behind the resistor, you should measure 7.5 V.
Similarly this works for all subsequent resistors: the 10k resistor will drop 5 V, which means that in front of it we have a level of 7.5 V (yellow), and behind it $7.5 V - 5 V = 2.5 V$ (green). Finally, the last resistor drops 2.5 V, bringing the voltage at the end down to 0 V (blue).
A: when electrical current flows through a circuit component (easy example: a resistor), the resistor dissipates power; as it does, the voltage decreases steadily from the high-voltage side to the low-voltage side. this decrease in voltage is called the voltage drop. 
In the case of a resistor of resistance R with a voltage difference across it of V volts, the power dissipated is equal to (V^2)/R. 
A: What exactly it means is, how much the opposition the circuit element is doing against the current flow..!!
If the circuit element has no resistance, meaning it doesn't oppose the current flow at all, the voltage drop across that element will be absolute zero. But that's true only for superconductor.
In all normal case all circuit elements will have some resistance and they oppose current flow and thus drops some voltage across them by obeying the Ohm's Law.
A: There is nothing special about the term "voltage drop" - it is just a voltage across a particular component or any part of a circuit. 
It is typically used in the context of a circuit with a known total voltage, in reference to voltages across specific parts of the circuit, especially, when we want to know how the total voltage is distributed between various parts of the circuit.  
Let's say, we have a battery that measures exactly $9$V. We connect it to a circuit consisting of two components connected in series, say, a resistor and an LED. 
A typical question here could be: "What is the voltage drop on the resistor?" or "What is the voltage drop on the diode?", which is the same as asking "What is the voltage across the resistor?" or "What is the voltage across the diode?".
Let's say, we measured those voltages and came up with $7$V on the resistor and $1.97$V on the LED. We re-measure the voltage on the battery and it is $8.98$V. So, we say that there is $0.02$V voltage drop on the internal resistance of the battery.
But that leaves $0.01$V unaccounted for. So, we say that there must be another $0.01$V voltage drop somewhere in the circuit, perhaps, on the long wires or on the contacts. 
A: Voltage is a term which is sometimes confusing because people use it different ways in different contexts. Technically, voltage is the difference in electrical potential between two points. Electric potential is a physics concept which describes how much potential energy will be added or removed from a system if a unit charge is added or removed.
For example, if the electric potential (I like to use the symbol $\phi$ for electric potential) at a point is 93 V, then adding a 1 coulomb charge at that point will add 93 J of potential energy to the system. Next, if we move that charge to a point where the potential is 100 V, we have effectively added 100 J but removed 93 J, for a net change of 7 J. The voltage, potential difference, ($V=\Delta \phi$) between those points is  +7 V. On the other hand, if we started with the charge at $\phi = $100 V potential point and moved it to the $\phi = $93 V potential point, we would have a voltage, $$V=\Delta\phi=\phi_{final}-\phi_{initial}=-7\text{ V}$$ and a potential energy decrease of 7 J. That potential energy is converted into some other form of energy, depending on the system.  This decrease of potential, or negative voltage, is commonly called a voltage drop.
I personally don't like adding the word "drop" to voltage. I simply say voltage, and I always emphasize which end of a circuit element is higher, because if the voltage "drops" going left to right, then it "rises" going right to left. The word voltage by itself is enough to convey a difference of potential.
