From Aegisub Manual
The attachment manager allows you to attach fonts and/or pictures to your script (by encoding them as text). This is especially useful for sharing fonts between everyone who is working on a script without having to send the fonts as separate files, for example.
The entire dialogue is fairly self-explanatory. The two "Attach ..." buttons add attachments, "Extract" extracts existing attachments into separate files, and "Delete" deletes attachments from the subtitles file.
Limitations and downsides
The SSA format specification only allows certain filetypes to be attached. For fonts, only .ttf is allowed. For pictures, .bmp, .gif, .ico, .jpg and .wmf are allowed (note the absence of .png).
Many SSA/ASS editors ignore or strip attachments. The original SubStation Alpha (v4.08) will work fine, but only for real SSA files. Sabbu will complain about unrecognized fields, and strip the attachments if you save the file. Most other editors either ignore the attachments or crash when encountering them.
A notable exception is mkvmerge, which will convert the attached files to Matroska attachments on muxing. If you demux the script again, the attachments will be stripped from the script, but they're still there as MKV attachments.
Unfortunately, storing binary data as text (in this case, a variant of UUEncoding) is not very efficient. The attached files will take considerably more space as script attachments than they do as separate files.