whats the black thin cable that runs off solenoid?

[omodos]

Hello, I am checking the connections on my starter as been having some slow statrup issues (loooooooong story)please can someone let me know the purpose of the black cable shown in the pic?it has play in it maximum 5mm up and down as in pic when i try by hand,what could the consequences be? could I just crimp or apply some pressure with small pliers to make it a tighter fit to what I guess is a spade connector type connection under the black sheath? it seems loose but wont come off and I dont want to force it off......thanks

PS Just looked on some bmw m3 site , could it be the solenoid trigger wire?