I will try to answer it a little bit more informally.
Connection timeout – is a time period within which a connection between a client and a server must be established. Suppose that you navigate your browser (client) to some website (server). What happens is that your browser starts to listen for a response message from that server but this response may never arrive for various reasons (e.g. server is offline). So if there is still no response from the server after X seconds, your browser will ‘give up’ on waiting, otherwise it might get stuck waiting for eternity.
Request timeout – as in the previous case where client wasn’t willing to wait for response from server for too long, server is not willing to keep unused connection alive for too long either. Once the connection between server and client has been established, client must periodically inform server that it is still there by sending information to that server. If client fails to send any information to server in a specified time, server simply drops this connection as it thinks that client is no longer there to communicate with it (why wasting resources meaninglessly).
Time to live (TTL) – is a value specified inside of a packet that is set when the packet is created (usually to 255) that tells how long the packet can be left alive in a network. As this packet goes through the network, it arrives at routers that sit on the path between the packet’s origin and its destination. Each time the router resends the packet, it also decrements its TTL value by 1 and if that value drops to 0, instead of resending the packet, router simply drops it as the packet is not supposed to live any longer. This mechanism is used to prevent network from flooding by data as each packet can live inside of it for only limited amount of ‘time’.