By default WinSCP performs files transfers and other operations on the foreground. This way it can use one connection to the server only all the time, however during the operation you cannot use WinSCP for any other task. Alternative way is to perform the operations on the background.
To instruct WinSCP to perform the transfer on background, check Transfer on background (add to transfer queue) on transfer options dialog before the transfer. If you do not use the dialog or want to transfer file on background by default, check Transfer on background by default on Background page of Preferences dialog. Also, you can drop files onto background transfers queue list to transfer them on background.
You can also move ongoing foreground transfer or delete operation to the background using Move to Background command. For the delete operation, this is only way to perform it on the background.
Once you instruct WinSCP to perform the operation on background, the operation is added at the end of the queue (visualized by background queue list).
WinSCP by default performs at most two background operations at once. If you schedule more operations, those will wait in the queue until some previous operation is finished. For each background operation WinSCP opens separate connection to the server using the same session option as used for the main session. Once the operation finishes the connection is kept on background and reused for future operations.
Once the background operation finishes, the target directory is reloaded (still on the background) and content of the respective file panel is refreshed.
Once you have your operations scheduled, you can use queue list to manage them.