We need negative numbers,
Say our bank balance is $6.
I do not know if the bank has $6 of my money OR if I have $6 of their money (a loan)
But if I say I have +$6 or -$6 then I would know which one I meant.
A better example
The temperature is 10 degrees celcius.
For me that is very cold but if you live in a very cold country that might be nice weather.
The temperature drops a long way. It gets way colder. It gets colder than 0 degrees celcius.
The temperature becomes negative. If we had no negative numbers we could not talk about temperatures any colder than 0. That would be really limiting. :)
The same happens when you talk about altitude above and below sea level. :)