What is claimed is:1. A cell-monitoring connector and a fuel cell having a structure for detachably mounting the cell-monitoring connector thereon, the fuel cell comprising:a plurality of separators arranged to be spaced apart from each other in a first direction, each of the plurality of separators including a receiving recess arranged in one side thereof; anda plurality of gaskets respectively disposed on the plurality of separators, wherein the gasket disposed on a corresponding one of the plurality of separators is spaced apart from and located around the receiving recess arranged in the corresponding one of the plurality of separators,wherein the cell-monitoring connector comprises:a housing, at least a portion of the housing being received in a receiving space defined by the receiving recess of each of the plurality of separators; anda plurality of connection terminals inserted into the housing, the plurality of connection terminals being connected to the plurality of separators, respectively, andwherein the housing comprises:a body inserted into the receiving space in a second direction that intersects the first direction, at least a portion of the body being received in the receiving space; anda lever portion comprising a latching protrusion configured to be movable when pressed in a third direction that intersects the first direction and the second direction, the latching protrusion being latched to or separated from a corresponding gasket among the plurality of gaskets.2. The cell-monitoring connector and the fuel cell according to claim 1, wherein the lever portion comprises a plurality of lever portions respectively connected to opposite sides of the body.3. The cell-monitoring connector and the fuel cell according to claim 1, wherein the receiving recess has a shape that is recessed inwards from an outer edge of each of the plurality of separators.4. The cell-monitoring connector and the fuel cell according to claim 1, wherein the cell-monitoring connector further comprises a terminal position assurance (TPA) detachably coupled to the housing, the TPA being configured such that the plurality of connection terminals are coupled into the housing in a press-fit manner.5. The cell-monitoring connector and the fuel cell according to claim 1, wherein the lever portion comprises:a first end portion configured to receive pressure, the first end portion being spaced apart from an upper side of the body in the third direction;a second end portion connected to a lower side of the body; anda wing portion disposed between the first end portion and the second end portion, the wing portion having a bent shape,wherein the latching protrusion is disposed on an outer side of the wing portion of the lever portion, andwherein the first end portion and the latching protrusion are configured to be movable in the third direction when pressed, with the second end portion as a support axis.6. The cell-monitoring connector and the fuel cell according to claim 5, wherein the latching protrusion comprises a plurality of latching protrusions spaced apart from each other at a regular interval in the first direction, andwherein each of the plurality of separators is arranged into a respective one of first slits defined between the plurality of latching protrusions spaced apart from each other in the first direction.7. The cell-monitoring connector and the fuel cell according to claim 6, wherein the lever portions include an insulating material.8. The cell-monitoring connector and the fuel cell according to claim 6, wherein the latching protrusions have a same thickness as each other in the first direction, andwherein the first slits have a same width as each other in the first direction.9. The cell-monitoring connector and the fuel cell according to claim 1, wherein the receiving recess comprises:a first side and a second side, facing each other in the third direction; anda third side arranged between the first side and the second side, the third side facing the cell-monitoring connector, andwherein the plurality of separators, each including the receiving recess having the first side, the second side, and the third side, are disposed to overlap each other in the first direction.10. The cell-monitoring connector and the fuel cell according to claim 9, wherein the plurality of gaskets comprise a first gasket and a second gasket, andwherein the first and second gaskets are disposed to face each other in the third direction with respect to the receiving recess.11. The cell-monitoring connector and the fuel cell according to claim 10, wherein each of the first and second gaskets has a hook shape, andthe hook shape of the first gasket and the hook shape of the second gasket are symmetrical to each other in the third direction with respect to the receiving recess.12. The cell-monitoring connector and the fuel cell according to claim 10, wherein each of the first and second gaskets comprises a first end facing the receiving recess in the third direction and a second end facing an outer edge of each of the plurality of separators in the second direction,wherein the first end is spaced apart from a respective one of the first and second sides of the receiving recess, andwherein the second end is spaced apart from the outer edge.13. The cell-monitoring connector and the fuel cell according to claim 10, wherein the fuel cell further comprises a shift-preventing part disposed on each of the plurality of separators and located in a vicinity of the third side of the receiving recess.14. The cell-monitoring connector and the fuel cell according to claim 13, wherein each of the plurality of separators comprises:a first region in which the first gasket is disposed;a second region in which the second gasket is disposed; anda third region in which the shift-preventing part is disposed,wherein the first region is contiguous with the first side of the receiving recess,wherein the second region is contiguous with the second side of the receiving recess, andwherein the third region is contiguous with the third side of the receiving recess and surrounds the receiving recess together with the first region and the second region of each of the plurality of separators.15. The cell-monitoring connector and the fuel cell according to claim 14, wherein the body of the housing comprises a shift-preventing groove to allow the shift-preventing part to be inserted into the shift-preventing groove in the second direction.16. The cell-monitoring connector and the fuel cell according to claim 15, wherein the plurality of gaskets comprise a third gasket including the shift-preventing part disposed in the third region of each of the plurality of separators, the third gasket having a straight line shape in the second direction and having a protrusion shape that protrudes in the first direction.17. The cell-monitoring connector and the fuel cell according to claim 16, wherein the third gasket comprises a third end facing the third side of the receiving recess, andwherein the third end of the third gasket is spaced apart from the receiving recess.