Bed frame slats are thin pieces of wood, often made of pine or similar wood. Sometimes they are provided as loose members and sometimes they are fixed together with strapping. You lay them on the top of the base, between the side rails, at regular intervals. They provide adequate support in most situations despite the gaps between the slats.
Sheets of medium density fibreboard are sometimes used instead of slats. Cut pieces as wide as the slats and lay them in the same place, on the support laths of the side rails. Butt adjacent pieces together leaving no gaps. Optionally, screw the MDF sheets into place. MDF sheets can provide a firmer and less springy alternative to slats, although they will add weight to the bed. This could make the bed more difficult to move, but this need not be a major problem.
Beds made in previous centuries, such as Shaker beds, often had ropes to support the mattress. The side rails were made of thicker wood than most bed rails today, as they needed to endure the tension of the ropes. Unless the ropes are very taut, the mattress on top of them will tend to sag in the centre. Rope beds are specialised items and not easily replicated by a non-professional.
You can use planed softwood -- whitewood or redwood -- instead of slats. Cut the timber to length and lay it where the slats should be. Use timber with a tongue and groove if you want it to fit together tightly. However, a simple butt joint between straight edged pieces is quite adequate. You can space out the pieces if you wish, leaving small gaps. Optionally nail or screw the pieces in place onto the laths of the side rails.
Reclaimed timber can also be used to replace slats. Sand it down before using it to ensure a clean and smooth surface. Metal beds often have a base made of metal mesh. The mesh can be of various sizes from fine to broad. The ends of the wires are often sealed into the frame for safety. A hammock bed uses fabric, netting or rope to support the weight of the sleeper.