Replacing switches with connecting wire
Hmmm a picture might help but here is what I think you have...

The second black wire that also attaches to the switch on the right is the hot feed to the two switches.

The other wires that come from these switches (black and red) feeds their respective light fixtures.

The unattached white wires that are just capped are neutral wires (return wires from the light fixtures to complete the circuits) they should be left as-is.

If you have a no contact voltage tester it should glow close to the wire that is the hot feed from the panel. The one that previously fed the left switch. Be careful while checking things with the power on. Leave them capped for this test.

The hot wire goes to one switch and a jumper is added to the other switch so both switches have a hot feed. Then each switch has a wire going to their respective light fixtures. One of them is apparently black and the other red. 

Hopefully this clarifies it a little for you.