A co-signer for a mortgage is technically a co-applicant, and the terms can be used interchangeably. To be a co-signer on a mortgage, you have to add all your information to the mortgage application and your income, liabilities and credit strength factor into the mortgage approval process. You also have to be on the title of the property being mortgaged as a legal owner (though your percentage of ownership can be as little as 1%).
The advantage of being a co-signer is that you have legal rights to the property and your name is on the mortgage contract. You can therefore request information from the mortgage lender at your discretion, and the property cannot be sold without your permission.
The disadvantage to being a co-signer is that the mortgage debt and monthly payments count against you if you later are applying for any other borrowing (purchasing other properties, vehicle loans, etc). There are also tax implications to consider: for example, when the property is sold there can be capital gains taxes payable on the appreciation in value (based on your percentage of ownership), since you as a co-signer it is typically not your primary residence.
Being a co-signer is sometimes compared against being a guarantor on a mortgage, which is a less secure position. See Guarantor for more information.