There are 2 protocols for email - pop and imap.
Lets assume you access your email theoug a program on the computer.
If the program accesses the email server via pop, then it takes the message from the email server and stores it on the computer - unless you have told it otherwise.
If it uses imap, then you are looking at your emails directly on the email server - so if you delete an email using the computer and then use another computer or tablet etc. to check the email you won't see the deleted email.