Figure of speech to help explaining a math term

Vector fields are commonly used to represent force fields, and the most familiar force field to students is the magnetic field. We can actually sense the magnetic field, if we are holding some magnetic object and moving it around in a magnetized area of space, and we experience it as an area with peculiar directional forces deployed. There's nothing weirder than feeling thin air press against the thing in your hand without moving.

Of course, it's not the air pushing, but that's the only material thing we can sense -- unless we think of the forces as individually invisible but real and powerful, and in motion, like electrons or atoms. That's pretty much what you want students to do. The mass and velocity and spin and magnetic moment and electric charge and other values are just measurements of those things (whatever they are) expressed in vectors (might as well mention tensors as the next step up, I spose, so they'll know the name, at least).

I'm interested in how far you're intending to go with vector spaces at this level of instruction. The really good perceptual metaphors involved in vector spaces are curl, div, and grad, and you need partial differentiation to get a handle on those.

n-dimensional Euclidean space, for example, is a vector space in which the ordered n-tuples (x1, x2, x3, …, xn), a.k.a. the coordinates of points in n-dimensional space, play the role of vectors. That is, they satisfy the properties of vectors in the usual sense if one considers the tail to start at the origin of coordinates and the tip to end at the coordinate (x1, x2, x3, …, xn). More broadly, a vector space is any set of elements whose members have the same properties as vectors. For n-dimensional Euclidean space, those elements are the n-tuples (x1, x2, x3, …, xn). Other vector spaces, i.e., sets, will have their own terminology for the members of the set. Another example is the set of polynomials of degree n, which compose a vector space of dimension n + 1. There is no one single name or figure of speech for the elements of a vector space.

Although I do agree with user Peter Shor concerning his claim that the OP's question doesn't belong to the present site, I'll still make the following answer as it could add something interesting to the subject.

In the concepts of everyday life there seems to be nothing tangible that will truly appear as having the nature of a vector space. The closest we might come to in the way of producing a vector space like entity could be found in the phenomenon of the opposition to current flow in an electrical circuit, where this opposition , called the impedance, is an ordered pair having for first element the resistance and for second element the reactance.
It is, however, grossly inadequate as a true vector space: there does exist positive and negative reactance (for equal magnitudes they cancel one another as do a vector and its inverse) but negative resistance is not a concept belonging to electricity; none of the would be vectors can have an inverse, multiplication by a negative scalar has no meaning at all. Except for this shortcoming we do have a componentwise addition and a multiplication by positive scalars for entities with the characteristic of being justified only by two components which are not of the same sort and not involving space.

Therefore, outside of the current examples of physics, where the components are homogeneous, except for relativity when to three components of space a time component is added to justify 4-dimensional space-time vectors, there seems to be nothing to talk to us of vectors in real life. On top of that, this example from electricity is still way too far removed from the realm of everyday life as the qualitative appreciation of the two effects still requires some understanding of many abstract concepts of physics. If we were nevertheless to refer to this phenomenon, we could then talk of a simile since there is no archetype of a vector space but only an approaching, crude model.

• A vector space is a system somewhat like an electrical series circuit with various points of opposition to current flow in it, there being at each of those points a variable resistance and a variable reactance that combine to produce a given impedance changing with time; the set of these oppositions to current flow under the operations of addition and multiplication by positive scalars has much of the nature of a vector space.

The combination of series impedances