Dropbox is an excellent tool to automatically synchronize your files from your computer to the cloud, and from there to others computers. Every file you put or modify on a Dropbox folder in your hard drive is uploaded to Dropbox, and from there to others Dropbox folders that you may have in others computers, linked with your Dropbox account.
The process is very simple and has many possibilities. If you aren’t aware of it or other similar services, I’d recommend you to spend ten minutes in a little research in this topic.
However, you must be carefully when using a program that opens files exclusively while working with them, like MS Word. In those cases, dropbox is unable to upload them until you close that program. It might happen that you hibernate or suspend your computer without closing the program; In this case, the file won’t be uploaded, and you will not have it in the cloud nor in other computers you use. Also, remember that uploading a file takes always some time. Wait until the little check mark turns green in the file icon, before leave to work in another PC.