A solid hardwood board is milled from one piece of wood and is typically 3/4" thick (although some come in 5/16" thickness). These products can only be installed on or above ground. Solid hardwood should not be installed below ground level, such as in a basement or walk-out basement because it can react strongly to moisture or high humidity.
A major benefit of solid hardwood is it can typically be sanded or refinished more than one time. It must be installed with nails, staples or glue.
An engineered hardwood floor is made up of layers (plies) of real wood that are adhered together to make the board more structurally stable than solid hardwood. Whether (and how many times) engineered hardwood can be sanded and refinished depends on the thickness of the top layer of wood. Refer to the warranty for your floor to determine the feasibility of being refinished.
A benefit of engineered hardwood is that it can be installed on any level, even in basements, and typically has multiple choices for installation, such as floating, gluing or nailing/stapling down.