When you're using a terminal program (something that provides a terminal window in a GUI environment, which is now the dominant form of 'terminals'), there's a fairly straightforward answer for what should happen when you hold down the Ctrl key while typing another key. For upper and lower case letters, the terminal program generates ASCII bytes 1 through 26, for Ctrl-[ you get byte 27 (ESC), and there are relatively standard versions of some other characters. For other characters, your specific terminal program may treat them as aliases for some of the ASCII control characters or ignore the Ctrl. All of this behavior is relatively standard from the days of serial terminals, and none of it helps terminal programs decide what should be generated when you hold down the Alt key while typing another key.

(A terminal program can hijack Alt-<key> to control its behavior, but people will generally find this hostile because they want to use Alt-<key> with things running inside the terminal program. In general, terminal programs are restricted to generating things at the character layer, where what they send has to fit in a sequence of bytes and be generally comprehensible to whatever is reading those bytes.)

Historically and even currently there have been three answers. The simplest answer is that Alt sets the 8th bit on what would otherwise be a seven-bit ASCII character. This behavior is basically a relic of the days when things actually were seven bit ASCII (at least in North America) and doing this wouldn't mangle things horribly (provided that the program inside the terminal understood this signal). As a result it's not too popular any more and I think it's basically died out.

The second answer is what I'll call the Emacs answer, which is that Alt plus another key generates ESC (Escape) and then the other key. This matches how Emacs handled its Meta key binding modifier (written 'M-...' in Emacs terminology) in the days of serial terminals; if an Emacs keybinding was M-a, you typed 'ESC a' to invoke it. Even today when we have real Alt keys and some programs could see a real Meta modifier (cf), basically every Emacs or Emacs-compatible system will accept ESC as the Meta prefix even if they're not running in a terminal.

(I started with Emacs sufficiently long ago that ESC-<key> is an ingrained reflex that I still sometimes use even though Alt is right there on my keyboard.)

The third answer is that Alt-<key> generates various accented or special characters in the terminal program's current locale (or in UTF-8, because that's increasingly hard-coded). Once upon a time this was the same as the first answer, because accented and special characters were whatever was found in the upper half of ASCII single-byte characters (bytes 128 to 255). These days, with people using UTF-8, it's generally different; for example, your Alt-a might generate 'á', but the actual UTF-8 representation of this single Unicode codepoint is actually two bytes, 0xc3 0xa1.

Some terminal programs still allow you to switch between the second and the third answers (Unix xterm is one such program and can even be switched on the fly, see the 'Meta sends Escape' option in the menu you get with Ctrl-<mouse button 1>). Others are hard-coded with the second answer, where Alt-<key> sends ESC <key>. My impression is that the second answer is basically the dominant one these days and only a few terminal programs even potentially support the third option.

PS: How xterm behaves can be host specific due to different default X resources settings on different hosts. Fedora makes xterm default to Alt-<key> sending ESC-<key>, while Ubuntu leaves it with the xterm code default of Alt creating accented characters.