This is already built into the file browser (Nautilus)! Only it's combined with another feature, so it isn't straightforwardly discoverable.
To encrypt, select one or more files. Right-click and select Compress. Pick one of the extensions that support encryption — I recommend
.7z. Mnemonic, so your family knows what format to pick: take the first item in the list. Expand “Other Options” and enter a password.
.zip has the advantage that the files can be read out of the box on Windows, but I don't know whether an encrypted file produced in this way uses the newer, strong encryption algorithm (based on AES and PBKDF2) or the older, broken algorithm (compatible with older software). So I recommend
.7z instead. The 7z format supports encryption (AES, with decent key stretching). Note that neither zip nor 7z provide cryptographic integrity verification (i.e. someone malicious can change the archive and it won't be detected).
On Ubuntu, make sure you have the p7zip or p7zip-full package installed. It provides the command line tool
p7zip package, supports only 7z archives) or
7z (supports most common archive formats as well). If you need this on Windows, 7-Zip is available (and is a good archive manager software beyond 7z format support).
To decrypt an archive, just expand it and enter the password when prompted.
Here's an illustrated tutorial.