Hi Irina, welcome to the forum
Is it real? That is the big question, and one which nobody can answer with 100% certainty. I think we all experience past life memories in our own way, and however 'real' they present themselves to us, not one of us can stand up and say "this is definately what happens to us after we die". If we could do that, then reincarnation would be a proven fact, and this forum would most likely not exist.
A lot of it comes down to faith. Personally, I can remember several past lives, and I am totally convinced that I have been here before. My memories place me back in time, in another body, in another place, and I'm there, reliving those moments with the same clarity as if I was actually there experiencing it right now, first hand.
I think one of the keys to believing is how these memories make you 'feel'. How do you experience your past life memories? Meditation? Dreams? Spontaneous? Do they leave you with a lingering emotion that can affect you for hours or even days after? And when you remember your past life, is it like an ordinary dream? Are all your senses heightened like smell, sight and sound are crystal clear? Do you have an inexplicable passion for a certain time period in history, or a famous historical figure? These are some of the signs that you might be experiencing a past life memory.
The best thing to do if you are that curious, is to start practicing meditation, and begin writing a journal of all your experiences. If this works for you, then slowly you'll begin to gather all the pieces of the puzzle, and hopefully things should fall into place. You might even find that 'clues' are all of a sudden ... mysteriously thrown into your path, as if the universe is willing you on to find out more. It really can be a fascinating and rewarding experience, and you've come to the right place to begin that journey
Here is a thread that may help you further:
Past Life Dreams - Common Characteristics