Transport which requires the cell to use energy in order to move things across a membrane is called active transport.
Active transport can occur in at least two forms; either the use of protein channels to "pump" a particle across the membrane, or by the use of vesicles, which are small membrane-bound structures that encapsulate the material being transported (although the use of energy in forming and assimilating vesicles is also a protein-mediated action, just as it is in protein transport). Moving against a concentration gradient tends to involve protein transport.
A concentration gradient is just a condensed way of describing the different amounts of solute that would be found in the different physical areas being considered in a given situation. Typically we look at the inside and outside of a cell, with the gradient being the relative high or low amount of solutes in either. Moving against a concentration gradient is just another way of saying that we're moving from low concentration to high.
Energy is required to move against the concentration gradient because it can be thought of as "pushing" against the force of the solute attempting to move down its concentration gradient, the same as one might feel resistance when trying to stuff clothes into a packed suitcase.