Bachelor's: this is also known as an undergraduate degree and normally takes three years to complete (180 credits). It is also referred to as first-cycle studies.
Master's: this is also known as a graduate degree. You take this after you have completed an undergraduate programme. It can be one or two years long (60/120 credits). It is also referred to as second-cycle studies.
PhD: this is also known as a doctoral degree. It is a research degree that can take several years to complete and that culminates in a dissertation. It is also referred to as third-cycle studies. (A licentiate degree also falls under the third-cycle category.)
You can find more detailed information about the different degree levels on the StudyinSweden webpage.