Legitimate interest is one of the six legal bases for data processing. Blackbaud’s document Important Impacts of GDPR gives a full and detailed answer on what legitimate interest is and how the GDPR will affect its use.
You may determine that your organisation is able to send communications to donors justified by a number of legal bases under GDPR. For example, you might justify sending 'Thank you's' on the basis of legitimate interest or sending tax receipts to your donors for their gifts on the basis of a legal obligation. Any communication or data processing would require that you've met one of the six legal bases of data processing.
We can't give you specific advice on determining when or where you should use this or it may apply to your organisation.
Nothing in this FAQ should be construed as legal advice or a legal opinion on any specific facts or circumstances