One of the things that spam filters look at when determining whether or not a message is spam is the IP address of the mail server from which the message was sent. Other attributes of the message, such as the sender's name and email address, can easily be faked or 'spoofed' by spammers. However, it is much more difficult to spoof the IP address of the mail server that is sending the message. Hence, spam filters often rely on 'IP reputation' of the sending mail server as a key factor for determining the likelihood of a message being spam. Spam filters often maintain 'blacklists' of IP addresses of mail servers known to regularly send spam messages, and 'whitelists' of mail servers known to never (or rarely) send spam messages.

Mail sent from a mail server that is known to have been used to send spam is likely to have a greater chance of being flagged as spam by spam filters at the receiving end. Thus, if you share a mail server with spammers, your (legitimate) mail is likely to have a greater chance of being flagged as spam by spam filters.

Mail servers will little or no IP reputation are often 'greylisted'. Many receiving mail servers will often initially defer mail sent from greylisted mail servers. Hence mail may be delayed because the sending mail server may have to make several retry attempts before the receiving mail server finally accepts the message.


Related:
Why do Legitimate (non-spam) Email Messages Sometime Not Reach Their Recipients
Why Mail Sent Through UltraSMTP is More Likely to be Delivered Successfully