If two quantum particles, e.g. two electrons, are entangled with each other, then these two particles cannot be considered as separate particles anymore. They behave like a closed unit, even if they are (infinitely) far apart from each other. The entanglement leads to the fact that an action at one of the two particles, can instantaneously influence the state of the other particle. Instantaneously means that no information transfer takes place. So one must not imagine that information is transferred through space and time from one particle to the other. There is no classical interaction between the entangled particles and yet an action on one particle affects its entangled partner. Entanglement is not limited to two parties, also multiple particles can be entangled.
In classical computing, the so-called logic gates, or gates for short, are physical components on a computer chip that process a binary input signal into a binary output signal. Usually, today's gates consist of transistors and the binary signals are voltage signals. On a classical processor there are very many of these gates. An example of a logic gate is the AND gate which outputs the binary value 1 if all input signals are 1, and outputs 0 if at least one input signal is 0. During the so-called compilation, a programmer's code is translated into machine language, i.e., into a sequence of instructions that are passed on to the processor. The processor executes these instructions with the help of the gates. These are so to say the last instance with which the original algorithm is implemented on the hardware.
Quanta are indivisible, thus elementary packages of which our world is composed. On the one hand, there are the building blocks of matter, such as electrons. On the other hand there are the elementary energy packages, the light quanta, also called light particles or photons.
In physics, it has been found that certain physical quantities, such as the energy of an electron in an atom or the electric charge, cannot be varied continuously, but can only take on discrete values that are multiples of an elementary quantity, i.e., multiple of a quantum. The quantity is said to be quantized.
Like classical gates, quantum gates process information and are, so to say, the last instance with which an algorithm is implemented on the hardware. An important example of a quantum gate is the Hadamard gate which transforms the binary values 0 and 1 into a superposition of 0 and 1, respectively. However, unlike classical gates, quantum gates are not physical components placed on the processor. While a classical processor consists of gates, the quantum processor consists of qubits (qubits can be realized, for example, with single atoms; the processor is then a regular arrangement of individual atoms). The quantum gates are physical operations which influence deterministically the state of the qubits on the processor (for example, a time-limited laser pulse used to exite an atom).
The quantum bit, or qubit, is the quantum-physical analogue of the classical bit, the elementary information carrier in classical information technology. The bit is the smallest storage and computing unit of conventional computers. These work with the binary system, that is information is encoded in sequences of zeros and ones. In a classical computer, for example, "power on" means a 1 and "power off" means a 0. If we consider a quantum system which classically can be in exactly two different states (e.g. excited and non-excited state of an electron in the atom), then we can use this system to realize a qubit. A qubit is the superposition of exactly two complementary states. In contrast to the classical bit, where one has either the state zero or one, the states zero and one are realized simultaneously in a qubit.
A quantum object can be in complementary states at the same time, that is in states which are mutually exclusive according to classical understanding. This is called "superposition" of states. For example, an electron can be in different places at the same time. But you could also put it differently and say that the electron simply does not have the property of being in a particular place. While in classical physics an object is always in a concrete state and has concrete properties, quantum physics allows these superpositions. Importantly, this superposition describes a physical property of the quantum object and has nothing to do with ignorance of the observer.