We all can make a difference, using whatever talents we have. At the same time, it's not clear the most practical thing from the US is to physically send books. It might make more sense to donate funds, and to donate books to local places that need them. Of course, there are more pressing needs to consider as well: food, water, shelter, safety. It can get overwhelming quickly. Here are a few resources that I found that have practical ideas for how you can help . . . and not all require money (signing a petition, for example.) They are all places to start. You may know of others.
The International Board on Books for Young People (IBBY) has a Children in Crisis Fund. They issued an Appeal for Syrian Children in Lebanon in 2013. If you are wondering, "why books?" then read here for a great explanation of what books can offer to children in times of crisis.
In other literary related news, look what Patrick Ness started & Philip Pullman, Anthony Horowitz, Cressida Cowell, Shannon Hale, Rainbow Rowell, Gayle Forman (and many others, forgive me for not naming you all) are doing in support of Save the Children. This is truly amazing -- I love the children's literature community!
You can also check out "Five practical ways you can help refugees trying to find safety in Europe" -- find a cause that speaks to your heart. There are plenty.
Presbyterian Disaster Assistance is responding to the European Refugee Crisis in Hungary. You can also find information about the ongoing crisis in Syria, including welcoming refugees in the US. (I include my church's connections; look to your own, if you have one.)
UNICEF has helpful resources for understanding as well:
The most important thing to remember is that you can do something. We all can.
Keep your heart and mind open.