What is the thing about heat that make particles vibrate faster? I'm just trying to understand the ultimate underlying dynamics of heat that causes temperature increase of, let's say, a liquid. Is it the electromagnetic radiation vector that moves between the fields and effects atoms? How can I exactly visualize this phenomena?
 A: 
I'm just trying to understand the ultimate underlying dynamics of heat
that causes temperature increase of, let's say, a liquid.

The ultimate dynamics is heat is energy transfer due solely to temperature difference. If the transfer results in a temperature change, it's because there has been a transfer of kinetic energy to or from the substance undergoing the temperature change. A visualization of what is going on can be seen here: http://www.hyperphysics.de/hyperphysics/hbase/thermo/temper2.html#c1
It is important to understand that heat can cause a change in molecular kinetic energy, but it is not the molecular kinetic energy itself. That is properly called the internal kinetic energy of the substance. It should also be noted that heat transfer may not result in a temperature change of the bodies involved. For example, heat transfer that causes the melting of ice or the boing of water at constant temperature. That heat is called "latent heat". Heat that causes a temperature change is often referred to as "sensible heat".
The three basic mechanisms of heat transfer are conduction, convection and electromagnetic radiation. The first two mechanisms require physical contact between the substances transferring heat (solids/liquids). The last (electromagnetic radiation) does not as energy can transfer in a vacuum. In this case, the increase/decrease in temperature is due to the absorption or release of electromagnetic energy.
Hope this helps.
A: Heat doesn't make particles move faster. It is particles moving faster. Not necessarily vibration (and certainly not vibration in a liquid). Heat is generally described as random thermal motions of particles. If particles are moving faster, they have more energy. That is the meaning of heat.
A: The core principle of heat is random particle motion. When we say something is hot, we are really saying that the particles it is made of are randomly bouncing around faster and when we say something is cold, we are really saying that its particles are randomly bouncing around slower.
Faster vibrations means that the particles that are doing the bouncing have greater kinetic energy; slower vibrations means less kinetic energy. So when you heat something up, you are increasing its energy content.
Heat gets transferred between particles when a faster (hotter) one bounces off a slower (cooler) one. The faster one slows down a bit (cools off) and the slower one speeds up a bit (heats up).
The exact details of this vary a bit depending on whether you are talking about gases, liquids, or solids, but the basics are the same.
A: The temperature of a liquid will rise if energy is being supplied to the liquid and its volume is not changing much (and I will assume there are no chemical reactions or things like that going on). This energy may arrive in the form of heat. That means it arrives in two main forms, called conduction and radiation. Energy can also move around when the liquid itself moves; this is called convection.
In your question you mention electromagnetic radiation, and this is indeed part of the complete picture (indeed most of it at high temperatures). If the electromagnetic waves emitted by some other body have a randomly oscillating component, then they will exert randomly oscillating forces on the particles of the liquid, and this causes them to jiggle about more. They vibrate, rotate and bump into one another. The technically correct name for all that motion is internal energy or thermal energy. The resulting more rapid random motion is the physical manifestation of a higher temperature.
The other main type of heat transfer process, and the one which often dominates at lower temperatures, is conduction of heat. In this case one part of some substance is hotter than another at first. So the particles in the hotter end are jiggling about more than those at the colder end. As those jiggling particles bump into one another the energy gets spread out more equally. The faster ones tend to end up giving up some energy, while the slower ones acquire some, just by ordinary collisions, but many of them. The net result is an overall transfer of energy from the hotter part to the colder part. We call this the conduction of heat. The overall rate of flow of energy is typically proportional to the gradient of the temperature profile.
