When you get a gift and keep it, you have to put it somewhere and then you have to remember where you put it. Each time you move to a new home, you have to pack the gift, then unpack it and put it in a new place that will also have to be remembered. Maude's action of throwing away the gift at the moment she got it meant she'll always remember exactly where it is, even though she will no longer have it.
The movie Harold & Maude is all about how age affects your perceptions of the world and of others. Young Harold sees a situation from one angle, but the elderly Maude looks at the same situation and has a totally different perception.
Maude has reached the age where possessions are not that important any more, but memories are. She's lived in many different places and has had many different things, and now realizes how ephemeral places and things are. But memories last as long as you do.