Looks like a transformer to me. What does the bottom look like Each wire should have a partner (other end) that you should be able to determine with an ohm meter There may be four different wires (up to eight connections from photo)
Most likely an inductor of some sort, from the shape.
At a guess, a common-mode choke in line with a power input connection - though there are various other possibilities, without seeing how it is interconnected with the rest of the circuit.
It looks like it was a common mode choke, a bifilar wound one. The tracking on the circuit board should confirm that, two connections in and two out, with one side connecting to a power input.
They are typically used for interference suppression, to reduce electrical noise passed back through power cables, that could otherwise act something like antennas.
That one has a toroidal core inside the casing. Without the case it would look rather like the one at the left of this photo: