つまらないものですが (tsumaranai mono desu ga) literally means “(this is) not interesting/exciting, but…” and is used when one gives a present to someone in a very humble way. Equivalent expressions in English would be “this is not much, but…”, “This is nothing special”, or “It’s just a little something”.
This phrase is often used by middle-aged people when they visit someone’s house and give them a gift. Since it’s not commonly used among young people, some people regard this phrase as a little old-fashioned.
This is not much, but … (I hope you’ll like it)
Oh you didn’t have to, thank you very much!