When you buy a home with someone else, among all of the other decisions, you will need to decide how you want to own the property: jointly, or in common.
Buying as joint tenants means that you both own the entire property. You are each responsible for everything, and each have the rights that go along with owning the whole property. It also means that, if one of you dies, the survivor becomes the sole owner of the entire property. Joint tenancy is usually the best way to take title if you are married or in a common law relationship, and buying a house together to live in together.
Buying as tenants in common means that you each own shares, so that if one owner dies, his or her share goes through his or her estate. Tenancy in common is usually the best way to take title if you are buying with a business partner, friend or sibling. It is also usually the best means if your parent has to go on title for financing purposes, but you will be putting in the majority of the down payment and making the regular expenses; you can own 99% of the property, with your parent owning 1%, to reflect who has the majority interest in the property.
The type of ownership you choose will depend on your personal situation and should be discussed with your lawyer before you sign your paperwork.