Both verbs mean "to be" but the key difference is in the permanence of what they are describing. "Ser" is used when you're describing an essential characteristic of the person or thing, whereas you'd use "Estar" for a more temporary condition or state.
If you're asking the question "What is she like?" the answer is likely to use "ser" as a response. If the question is "How is she today?" then it would be "estar". For example: Es callada (she is a quiet person) vs Está callada hoy (she is quiet today).
Ser is also used for: Possession, (el libro es mío), Occupation (yo soy marinero), Origin (yo soy de Inglaterra), Relationships (Ella es mi madre), Time (son las cinco de la tarde) and Impersonal phrases (aprender Español es divertido).
As we've discussed Estar is used for temporary state but also for: Location or Position (Está en el baño) and Ongoing Actions in the progressive tense (Estoy lavando los platos).
There are a number of adjectives in Spanish that have a different meaning depending on whether you use Ser or Estar. For example "Estoy aburrido" (I'm bored) vs "Soy aburrido" (I'm boring), so it's a good thing to get right!