It means "I understand" but also can imply that one has gone through the same experience and so has a definite feeling ( sympathy) for a common experience

'I can relate to . .'  means  'I understand . .'

“I can relate” is more personal than “I understand”. “I understand” is rational. You might have not had the same experience but can understand what the other person is saying. “I can relate” means you have had the same experience or a similar one and therefore know how it feels.