If it is a whole folder you want to transfer, you can use Menu > File > Export > Export to .eml files, then select the folder or multiple folders. If it is just a few messages you can select the messages and right-click > Save As. On the other computer use Menu > File > Import > Email (.eml), or drag the saved files from Windows Explorer to the desired location in eM Client.
If you want to move the whole eM Client to another computer, use Menu > File Backup. On the other computer use Menu > File > Restore. The will duplicate what was on the previous computer, so will completely replace all data on the destination computer!