Reflowing a motherboard (the main circuit board in your PC) is where they redo the solder connections.
As the solder connections get older they will oxidize and crack and may lose their connection thereby making your PC (desktop or laptop) either not work or not work correctly.
This can be done in two different ways. One is by applying heat to each connection on the board and basically re-melting and cooling the connection. A soldering iron is used to do this. The person doing it has to be careful not to damage electronic piece attached or to short connections. The second way is to heat the whole board (with meltable parts and burnable parts removed) in an oven and cause the solder spots to flex and reset with full connectivity.
I would suggest having a professional do this either way. I have never done a reflow. Usually when there are connectivity issues in the PC I have found an easier step usually solves it. That is removing and reinstalling all cards and plug connections in the PC. These will oxidize also and can get dirt in them also preventing connection.