A cost is what a firm, an individual or society pays to produce or consume goods and services. It is the consumption of resources such as labour time, capital, materials, fuels, etc. In economics, all resources are valued at their opportunity cost, which is the value of the alternative use of the resources. Costs are defined in a variety of ways and under a variety of assumptions that affect their value. The opposite of a cost is a benefit and often both are considered together. For example, net cost is the difference between gross costs and benefits.
Marginal cost is the cost of adding one additional unit of output or the cost of increasing an activity. It is the change in the total cost ( TC) divided by the change in output ( Q). This can also be expressed as the variable cost ( VC) divided by the change in output ( Q). This is because the fixed cost doesn't change, but the total cost (TC) will alter in sync with the variable cost (VC).
Essentially, this is how much it costs to produce or consume one more unit of something. To see what this looks like in the context of a firm, see: costs for a firm.