Yes, of course a mother can breastfeed twins or triplets. Many have exclusively breastfed multiple infants for their first six months. Others have partially breastfed for a variety of babies- or mother-related physical and social reasons. Some doctors believe it isn't possible to exclusively breastfeed multiples, but that isn't true. I suspect that whoever says this hasn't seen it with patients because they have created a self-fulfilling prophecy. And those who really wanted their babies to get only their milk probably sought a more pro-breastfeeding doctor.)
Breast milk production depends on milk removal. The more milk that's removed (and more is removed by twice as many babies), the more milk a mother produces. “Demand” drives supply. So your supply is meant to keep up with your babies. However, a small percentage of mothers may be affected by physical conditions that negatively affect this process. Talk to a lactation consultant to discuss any concerns you may have.
Milk removal depends on each baby's ability to effectively breastfeed. When babies are born, even a bit early as twins often are, they may not be mature enough to effectively breastfeed. Some are too sleepy and others breastfeed well but can't do it long enough to remove enough milk. They will get there with practice, but a mother will need to pump her milk after feedings until each baby does breastfeed well. This milk can then be used to supplement feedings. (Mothers tend to obtain more milk in less time when using a hospital-grade rental pump for this kind of situation. Time is essential when caring for two or more newborns.)
When at least one baby learns to latch onto the breast fairly easily and breastfeeds well, breastfeeding two at the same time — called simultaneous feeding — may save time and tears. Some full-term twins and their mother are ready to breastfeed simultaneously on the day of birth, but often it takes days or weeks before mother and babies are ready or able to accomplish this without help. Until then, a helper can help support one or both babies until each is latched on. This can make it easier for you to feed two at once.