Went through all the process, finally I got a PhD studentship offer. I was excited for last two weeks. But recently someone told me better to give it up and search for better university to do PhD. I did my master in a top university, but the PhD university's ranking is very low. Does the reputation really matter for doing a PhD?

if you've got a very good supervisor then i don't think it matters that much, but undeniably, it does matter to some extent how good the uni is. in most cases after you get your first job after the phd, it becomes less important where you did it as long as you can prove yourself as being good in your field, either thro publishing or something like that.

As I have read here before, what matters the most is the RAE rating of the department rather than the university one. Here is the link for RAE if you need it. http://www.hero.ac.uk/rae/Results/

The department and supervisor is the important thing.

Yes ranking does matter a bit. More importantly you need to be sure it is the research you want to do, and then look at the qualities of the supervisor and dept. to allow you to do it. Ask them about Job placement rates etc. It could also be that the person that told you this was jealous...

Your publications and quality of research you produce will matter most.