Mail accounts have two separate sets of credentials and settings. One set of credentials for inbound (receiving) mail and which is also used for accessing any mail you've saved on your ISP mail server — the POP or IMAP protocol is used for accessing that information on the mail server — and one set of credentials for outbound (sending) email messages out — a protocol known as SMTP is used for that access into the server.
Your outgoing email settings are likely incorrect; here is Apple's support document (TS3276)
You can use the Connection Doctor (Mail.app Window > Connection Doctor) to get (and show details) but your description certainly seems that your outbound (SMTP) settings — server name, port, username, password, whether SSL/TLS is disabled (unlikely) or enabled (likely) — don't match what your mail ISP requires.
In Mail.app, the inbound (POP or IMAP) mail account settings are easy to find. Mail.app Mail > Preferences > Accounts > Account Information. The sending (SMTP)Nsettings are buried, and you have to select the inbound (POP or IMAP) settings (Mail.app Mail > Preferences > Accounts > Account Information) and then switch the Outbound SMTP Server pop-up setting to its Edit SMTP Server List setting, and you'll get a whole different set of settings shown. Select the SMTP server for your ISP from the list, and then edit the settings to match the requirements.
I unfortunately can't tell you what the settings need to be, because the required settings can and do differ by ISP.
Thank you v much for taking the time to show me this.
I have gone into acc information and seen the incoming server is pop3.live.com and the outgoing mail server showed hotmail but when I went into Edit SMTP server list it had a different server so I typed in pop3.live.com
Was this the right thing to do? I still can't send an email.
Do I need to log out and try again??
Thanks for your help
Settings are specific to the mail provider.
Which mail provider are you using? The Microsoft Live / Hotmail / Outlook.com stuff, based on those hosts?
Each specific provider usually has set-up instructions posted. Somewhere. If you can identify and confirm which provider you're using, I or somebody else can look around for those settings and those instructions.
If your provider offers web mail access, that's often where you can log in (via the web interface and your username and password) and (usually via some link posted somewhere around your web mail account settings web page) find a link to the POP or IMAP settings, and the SMTP settings, for your particular account. (While many providers do have this, not all providers offer this information, unfortunately.)
Changing the sending and receiving computer server settings to match, that won't work. There are two sets of credentials, and both have to be correct, and both have to match the specific requirements of the particular provider.
More often than not, the sending-related settings and the receiving-related settings will differ. Different computers will usually be used for sending and for receiving mail. Having the same settings would make things far too easy (for everybody) after all, and Apple and everybody else maintaining mail clients could just get rid of one clump of settings, and everybody using and configuring those clients would rejoice.
Alas, that sort of mail setting configuration consolidation is very unlikely to happen. At least, not anytime soon.
Rebooting or restarting Mail.app? That's unlikely to change how Mail.app operates. Mail.app accepts and uses the changes immediately after they're input and you've confirmed saving the changes.