Normally, anybody over the age of 18 who rents or owns a property is responsible to pay council tax. If you live with a partner you will both be individually responsible for the whole amount of the council tax, if the other person doesn't pay it.
Councils talk about this responsibility as "liability for council tax" and they talk about people being "liable", i.e. responsible, to pay the council tax.
Are you liable for paying the council tax?