The charge cancels out, but that doesn't mean they can't stay put. Imagine a positive charge in the middle of a triangle and three smaller identical negative charges in the corners, for instance.

In reality it's a bit more complex than that. Electrons are fermions, and that means that they experience so-called Pauli repulsion. This is what prevents two atoms from falling on top of one another, and what prevents you from inserting your hand into the table. On top of that there are dynamical electromagnetic effects, known as dispersion, that lead to electromagnetic attraction even between uncharged objects. For instance two atoms of argon, both neutral, will attract one another unless they are very close to one another.

In an iron lattice the cohesion is due to the electrons stabilizing the nuclei.