I'm going to take a different approach, starting with chords, and moving to key.

You're right, chords are multiple notes heard at the same time. The study of how those notes interact is called Harmony. Chords can be simple, or really complex. But they generally we can separate them into two types: notes that sound good together are called consonant, and notes that sound like they are fighting or are unpleasant together are called dissonant. That's right, the word harmony doesn't mean pleasant, harmonies can be pleasant or unpleasant (consonant or dissonant).

Now, in a piece of music not all chords are equal. In the vast majority of the music you are exposed to is called "Tonal" music. This means that there is a note or chord which feels like home. Music is like writing a story; if there isn't a final ending to the story, it just feels wrong. As you said, you are aware of do re mi fa sol la ti do. That's a great example. If you were to sing or play those notes, and stop on ti, it can be painfully incomplete. I like to demonstrate this in class. I'll play those notes and stop before the final Do, and the whole class squirms, or tells me "Finish it!" I've even had students run up to the piano and play it themself.

You can think it like grammar and punctuation. Sentences can end in a question mark, or a period. One feels incomplete, the other feels complete. In tonal music, there are all sorts of ways to point to the chord or note which is "home." It's all about tension and resolution. It's a lot like writing a book. You introduce your main character (establish the key), go on some adventures (different chords, chords with tension), and finally conclude the story (returning to the home key).

Take note: this is a description of tonal, western music. India for instance, has a long history of its own classical music, that uses different expectations and tools.