It is an old type of wiring common in old house – but it still might be fine.
It is a predecessor to modern house wiring (Romex). We can distinguished two types of wiring in this case – first has a ground conductor the other one does not.
If you have a type without an extra ground wire it is not possible for you to install a three prong receptacles without ground fault protection. Such a type of wiring are old. It hasn’t been installed in houses for 50+ years. It construction consists of rubberized insulation and paper and due to this it is very likely to degraded by now.
When you have such a kind of wiring let it be evaluated by a professional to give an opinion on its integrity, and if you can do to mitigate any fire risk or it requires to be redone.
The other kind of cloth wire comes with grounding conductor or so called “ground” by most of people. This wire is better than the cloth wire of first type. You can upgrade this to three prong receptacles and such a wire is a bit safer.
BUT be careful I recommend you to have it evaluated to determine if insulation is rotting.
When you move the wires in your box and the insulation starts falling it means that you should do something with it and call a specialist. Caution – there is a real fire risk if it happens.
Remember an old house with old wiring always requires a professional evaluation to make a plan to make it safe for your family.
The other scenario is that the wiring is fine and you don’t need to update it. Anyway you may not have enough circuits and this is why you have tripping breakers. Often a solution is simple and adding new circuits to take some load off the existing ones can be really helpful.
Arc fault breakers are inexpensive in short time solution in fireproofing your cloth wiring. They open the circuit way faster than a normal breaker should do. This can be solution until new circuits are to be replacing the old ones.