Yes MRSA is very contagious and can spread from person to person through skin to skin contact.
If you touch someone's clothing or bedding with your bare hands then you can also get MRSA so you should wear gloves when handling someone's clothes or bedding.
And wash your hands after you remove your gloves or have been in contact with someone who has MRSA.
MRSA itself is not serious.
However when MRSA is left untreated the MRSA can become dangerous as it can lead to more serious infections that can lead to death.
MRSA stands for "Methicillin-resistant Staphylococcus aureus" which is a staph bacteria that in itself is usually harmless but MRSA almost always leads to more serious infections in those that are not treated for it.
MRSA is also a cause of a staph infection that is difficult to treat because of resistance to some antibiotics.
Some MRSA infections can be life threatening so you should always get medical attention and treatment for the MRSA before it gets worse.