Capex is short for Capital Expenditure, which is investment made to undertake new projects. So for example the money spent in building a new power plant. In accounting terms, capital spending is then “capitalized”: the newly built asset is listed on the company’s balance sheet and depreciated over its useful life.
In the energy business, e.g. when referring to something like a new power plant, capex tends to be used synonymously with terms like “installed cost” and “investment cost” in referring to money spent now to build the plant – as separate from money spent in future for the operation of the plant (e.g. opex).
It’s often expressed using the metric “$ per Watt” (or m$ per MW) to compare the costs of building different types of power capacity: e.g. 100MW at $2/W means an installed cost of $200m.