Well, about the concept, Coulomb experimentally determined that the force of interaction between two charges has a magnitude of ##k\frac{qQ}{r^2}##, where ##k## is a constant, ##r## is the distance between them, and ##q## and ##Q## are respectively the charges' "charges".
One then imagines this: If I have just one charge, ##Q##, then I can imagine that it creates a "field" such that if I place another charge anywhere, then the force between the two would be as already mentioned.
That field would have a magnitude of ##E=\frac{F}{q}=k\frac{Q}{r^2}##, where we, now, interpret ##r## as the distance to any given point in space, thus you have a function of position.
In vector form, you would have ##\vec E(x, y, z)=k\frac{Q}{(Q_x-x)^2+(Q_y-y)^2+(Q_z-z)^2}\vec u##, where ##\vec u## is the unit vector of the line connecting the "fixed" charge (the one "generating" the field) and the point ##(x, y, z)##, and ##Q_i## are the charge's coordinates.
For your exercise, you need to consider another fact, which is that you can add fields, so that if you have ##n## charges, then the electric field at any point is the sum of all electric field. You can also consider infinitesimal charges, i.e infinitely small parts of a "total" charge.
The wire is your "total" charge, you need to consider it being formed of infinitely many infinitesimal charges ##dq##, and that the magnitude of the field generated by any of these is ##k\frac{dq}{r^2}##.
This a really watered down summary of your lecture, you should go read the textbook and look at examples. I recommend Michel van Bizen's channel.
Here's a link to the chapter you are currently studying.
