see friend, let us be clear about what we call 'dimension'. in physics we often (almost always) talk of vectors. if the vector you are considering can be written uniquely in terms of some convienient set of vectors which are independent of each other, i.e any of them can not be written in terms of the rest, then the number of such independent vectors is called 'dimension'. For example, let
dispalcement vector A=3 i + 4 j +5 k, be a vector written in cartesian form, where (3,4,5) are its coordiantes, and i,j and k form the reference vectors. because your three reference vectors i,j and k are independent we say that A is defined in three dimensional 'world', the hence cartesian space is '3 D', or more adequately it is 3 D vector space. Now, for modeling the newton's laws this 3 D space was found to be adequate and so abundance of 3 D is found. now if i begin with writing some vector f in terms vectors a, b, c, d, e, f with all of them independent then i am constructing a six d vector space !!
i do not know what my f represents physically but still my space is there ! things like these form what is called linear algebra in mathematics/mathematical physics, and have independent existence. amusingly in quantum mechanics one often works in infinite dimensional vector space !! there the vector space needed to understand simple harmonic oscillator is also infinite dimensional..... !!!!!!!!. so there nothing very physical about dimensions.
now let me come to your answer. while studying maxwell equations in electrodynamics, lorentz discovered that the magnitude of usual position vector r changes under rotations of this vector, that is maxwell equations do not fit with the vector space of three d. so he fitted the problem by making a four d space with coordinates x, y, z, as usual and c*t as new addition, where c is speed of light and t is time. this was consistent with the maxwell eqns. and in this manner it forms more general representation for explaning any phenomena. now it is this vector space which is refered as 4 D space, and t as 4th d (simply forgetting about c because it is a constant any way). people often confuse t with role of x,y and z. remember, t is simply a parameter which specify the degree of disorder in your system, that is all, it can not be controlled at will and always changes whether what or not you want !?!
so in that sense there is nothing really "fourth" about it.
i hope that you understood, and if you are serious physics student/professional then please do not read popular science books, because they do not depicit the ground reality, instead go for good textbooks it may take more time/effort but then you will end up learning more !!
sorry for such along, and complicated answer, if you find it boring please ignore it.