Anthology. A collection of stories in a book, written by one author or several authors. Often if the stories are by a single author, that author is already well-known. If the stories are collected from a number of different authors, they may be on a specific theme or a specific genre. Some anthologies are a collection of stories already in public domain. In that case, you would not have to seek permission to include them, but would still need to give the original authors credit (listing their names in the bylines for their stories). If the anthology was your idea and you contact prospective publishers, you would be considered the editor of the project. Once you find an interested publisher, it will be your job to work out the terms, such as royalties, how much (if any) the contributors will receive, terms regarding contributors receiving free books or purchasing books for resale, who pays permission fees, etc.
As the editor, you will need to make decisions such as how many stories you will accept, will you accept reprints or must they be original, what kind of compensation will the contributors receive, length of submissions, theme or topics to be covered, format for the book, and any other decisions specific to your particular project. If you are including material quoted from copyrighted sources, you will be responsible to seek permissions and pay any necessary fees (unless the publisher has agreed to pay them). You will also need to compile the list of permissions for an acknowledgments page at the front of the book. Those who give these permissions generally ask that the acknowledgment be written in a specific way or format. Be sure you list each permission as they have indicated. For tips on creating an effective anthology, go to: http://www.writersdigest.com/editor-blogs/guide-to-literary-agents/hearing-voices-6-steps-i-used-for-creating-an-anthology.