best way to handle many wifi connections in a small or medium office environment?

Hello, I'm not that knowledgeable, would I be correct in believing that rather than a a single wireless router, what would be needed in this case would be like an ethernet router connected via ethernet to various wireless Access Points placed throughout an office and this would allow many wifi connections? Does the number of these connections increase with each Access Point placed or is it limited by the router itself ? Also what exactly is a mesh network? Does it let you switch seamlessly from one network to another or something like that ?