Series connection: Electric cells are combined in such a manner that positive terminal of one cell is connected to the negative terminal of another cell. Here, total emf of the circuit is equal to the sum of emf's of all the cells.
Parallel connection: Electric cells are combined in such a manner that positive terminal and negative terminal of one cell are connected to the positive terminal and the negative terminal of another cell respectively (provided, all cells have the same emf). Here, total emf of the circuit is equal to the emf of a single cell.