It’s important to realize how eM Client works with IMAP: it only downloads message headers by default to make synchronization more efficient and to save space on your device.
Messages themselves are fully downloaded once you click on them to show their content in eM Client. Thus, eM Client cannot search in the bodies of all your messages by default.

If you’d like to search inside the messages, you can download your messages for offline use.
This setting is available in Menu > Accounts - the account that you’d like to download the emails for - IMAP tab - Offline - "Download messages for offline use".
You can also include images and attachments (if you want to search inside text attachments).

POP and EWS accounts download full messages automatically.