You'd say this, for example, if you and a colleague are both working on different aspects of the same project, and you wanted to ask how he/she was progressing. 'How are things moving along...?' means 'How are things progressing...?' and '...at your end' ' is a fairly vague term meaning 'where you are' or 'what you are doing.'

Hello Evandro, This expression ("How are things moving along on your end") usually means that the person is asking for a status update on a particular project. Perhaps the person gave you an update about their part of a project, and the person now wants to learn about the progress you have made on your part of the project. This is a fairly common expression between two people who work together, but do not see each other frequently.

I am guessing this is a work situation, where you and your colleague are working on some kind of project. He is asking for the status. "On your end" means "your part of the project".

Depending on the context, it can simply mean 'how are things with you?'. But, for example, they maybe talking about a specific topic such as a piece of schoolwork, or a project or are inquiring about any updates on the other persons situation.