The verb tolerate means "to put up with or allow." You can tolerate your sister's love of Broadway musicals but really, you prefer dramas.
Think of tolerate as the open-minded verb. It means you allow something to happen or exist, even if you don't really like it. For example, you don't like your neighbor's loud music but you tolerate because he only blasts it on Saturday afternoons. Scientifically speaking, when your body can tolerate a drug, poison or even pollution, it means you aren't harmed by it.