A field is function that assigns a value to every point in a space. The space is in general just an abstract mathematical space but in physics it is often the physical space we live in together with time.
The air temperature on earth is a field, a function that takes a position on the ground, a height above ground, and a time and returns the temperature at that point and time. And so is the wind velocity, just that the value of the function is not the temperature, a single number also called a scalar, but a vector pointing in the direction of the wind and with a length proportional to the wind speed. Temperature is therefore called a scalar field, wind velocity a vector field, and there or other kinds of fields like tensor fields, for example, which are a generalization of scalar and vector fields.
It's a mathematical construct that is a core part of the theory physicists use to make highly accurate predictions about many of the low-level dynamics of reality.
It seems to usually be visualized as 2d plane-like sheet that can oscillate, and those oscillations represent particles. In reality it should be 3d, but that is much harder to draw.
So if objects are just perturbation in a field, and field is a mathematical construct, just like the concept of a number, or a line or a circle, then isn't it meaning less to look for a start for the existence of a field, and hence the whole universe?
No, for a couple of reasons. It's a mathematical construct used to describe observed phenomena, the phenomena itself isn't necessarily that similar to the construct. Further, it may be a terrible description.
A sinus is a field, deductively reduced to lower dimensions, e.g. a slice cut of a sound wave. Waves on the sea form a wave field, figuratively, and it extends to the bottom of the sea. Whereas a quantum field is a consequence of the Schroedinger Wave equation positing that the potential to observe a particle is distributed in space. As far as I know that's purely virtual, because observation of the particle collapses the potential. The crux is, the observation is not exact; The location of the particle is a probability distribution over a field as well. So ... it's fields all the way down. I'm not an expert, just stipulating.
Intuitively, if you're in a field, you get pulled in a different direction and/or amount depending where you are[1]. Except the meaning of the vector "pulling" on you might not be displacement of position. At a disco, for instance, you could think of the light creating a field that pulls your hair through the space of colors.
[1]Unless it's a constant field, in which case you'll feel the same pull no matter where you go.
