You're modifying only a local automatic variable m in your function. C is a pass-by-value language. If you want to pass by address, then an address is what you have to pass, declaring the formal parameter as a pointer-to-type, even when that type is already a pointer and what you're modifying is the the pointer itself.
When you're passing something as an in/out or out parameter, If you find yourself doing this:
void foo(Type *p)
{
    p = malloc(...)
}
you're not modifying the data pointed to by p, you're modifying p itself, and the caller will be unaware of the change. The address stored in p upon entrance is lost. Where as this:
void foo(Type *p)
{
    *p = ....
}
is modifying what p points to. That said, if Type is already a pointer-type, and what you want to modify it the pointer itself, you must do this:
void foo(Type **pp) // declare a pointer-to-pointer-to-type
{
    *pp = malloc(....) // dereference to store the address returned from malloc
                       // in the pointer pointed to by pp
}
Therefore, the most immediate fix is to declare the formal parameter as a pointer-to-pointer-to-type, passing the address of matr from main()
void initMatrix(Matrix_t **pp, size_t s) 
{
    int i;
    Matrix_t *m = malloc(sizeof(Matrix_t));
    m->content = malloc(s*sizeof(float*));
    for(i=0;i<s;i++)
        m->content[i] = malloc(s*sizeof(float));
    m->size = s;
    *pp = m; // note: saving pointer to the output target
}
int main(int argc, char** argv) 
{
    Matrix_t* matr = NULL;
    initMatrix(&matr,s); // note: passing address of pointer
    /*
    ...
    ...
    ...
    */
    return 0;
}
I left out the error checking (or I should say, I didn't add any, as there was none there to begin with) and removed the unneeded casts from malloc, which you can read more about here.
There are about a half-dozen ways to do this, but this is the most direct to what code you already have. I would advise either returning the allocation from the function itself as the ret-val, or not even dynamic-allocating the structure itself as there is no need to do so. Both of which I leave for you to think about.
Best of luck.