It's a very common and versatile expression used to apologize for:
* Mistakes: "Lo siento, rompí tu vaso" (I'm sorry, I broke your glass)
* Offending someone: "Lo siento, no quise ofenderte" (I'm sorry, I didn't mean to offend you)
* Causing inconvenience: "Lo siento, llego tarde" (I'm sorry, I'm late)
* Expressing empathy: "Lo siento mucho por tu pérdida" (I'm so sorry for your loss)
You can also use "lo siento" to politely decline something or express regret: "Lo siento, no puedo ir" (I'm sorry, I can't go).