For people who don't know the difference between cement, mortar and concrete: Cement is a substance used for producing mortar and concrete. It's never used on its own. It is a "binding agent". Note that the term "cement" is often not used correctly in everyday speech, with people talking about gluing bricks together with cement, when bricks are actually glued together with mortar. Mortar is the glue between bricks. Y…
Not a correction per se, but some further explanation.
The reason for reinforcement is because concrete is strong in compression and weak in tension - in fact for design purposes we disregard its tensile capacity entirely. What reinforcement does is handle the tensile stresses in a structural member. When a beam, column, or slab bends it often (based on the load placed and structural design) creates tension on one side and compression on the other, so we put the rebar in the structural member close to the tension side, or on both sides if there may be tension on both sides.
In slabs reinforcing may also be used in some capacity just to limit cracking in an otherwise non structural capacity. In certain kinds of designs it may also provide confinement to the concrete which can be important for structural analysis reasons that are too technical to get into here (plastic hinging especially in earthquake design, etc).
We have different kinds of reinforcement, depending on the need of the project, but for the most part we use steel because its reasonably durable, has similar temperature expansion properties to concrete (imagine if your concrete got cold and shrunk more than things embedded in it, or grew so much the things embedded in it weren't attached anymore), its behaviour is well understood, and it is reasonably priced.
The design of steel reinforcing in concrete is also done in a way that reduces the likelihood of sudden failures, so that if something does happen, it happens slowly and with plenty of warning.
There are alternative reinforcing materials that may be appropriate in some very specific situations, but civil engineering moves very slowly and adoption is slow because risk is high. Fiber Reinforced Polymer (FRP) and Glass Reinforced Plastic (GRP) are examples of these. They may have much higher tensile stress capacity per unit of area, and also are less susceptible to corrosion, but they cost a lot, their failure modes are sudden, greater deflections under load, and each may have other tradeoffs like worse compressive behaviour, or worse fire resistance, etc.