In my home, I have a small shrine to my ancestors and beloved dead. It is nothing fancy but it serves an important function. My shrine (which now includes a prayer card for my recently deceased paternal grandmother) is a place where I interact with the dead who are close to my heart and who have come before me. It is a place where I may honor them and give them gifts. It is, I hope, going to be a place where my sons will come to cherish as they learn the value of honoring their ancestors.
Some people would argue that it is foolish to keep a shrine to the dead. These are often the same people who get uncomfortable when you mention anything that is not Anglo-Saxon Protestant Christianity. It is important, however, to know your roots and where you come from. It is important to honor those who came before you and laid the groundwork for your very existence. As one random person on the internet said, "You are the result of the love of thousands."
Sometimes the ancestors who are close to you in time are not people you wish to interact with. That's ok. Because for every ancestor who was a rotten person, there is another who was a very good one. You may not know those ancestors' names. Don't let that stop you from expressing your appreciation for them. Don't let it stop you from seeking out their assistance and wisdom. Just as the gods communicate with us by way of signs, so too does the dead. Some people are lucky enough to psychically see the ones who wish to communicate with them or to 'hear' their voice. Most people, however, get their messages by way of synchronicity and random happenstances that only make sense in the context of their perspective.
Honoring your ancestors brings them comfort of knowing that they are not forgotten in this world. Giving them gifts and offerings (such as flowers, food, and drink) makes the spirit world easier for them and a happier place. It also opens the bridge between you wider because it makes you more receptive to their efforts to communicate. Your ancestors want to interact with you. They want to know that they are remembered in this world and they want to help you achieve the greatest good you can in your life. They want to see you successful and happy, because that strengthens the line and leads to greater success in future descendents.