It ChatSecure is an XMPP client; XMPP being an open federated protocol.
Signal uses Google infrastructure; while this isn't an issue for security purposes (because everything is encrypted), some people don't like it, some people like to run their own servers. With a "centralized" protocol like Signal, running your own server means you are cut off from everyone on the main server; with a "federated" protocol like XMPP your server can communicate with the other servers, so you can chat with users on other servers.
The innovation with ChatSecure over other XMPP clients is that it has implemented an XMPP extension (XMPP is an extensible protocol) called "OMEMO" that implements encryption, by borrowing substantially from the Signal protocol. This is an improvement over OTR, the status-quo way of doing encrypted XMPP, which the linked page explains was designed around desktop usage and doesn't work well with phones.