Learn Portuguese (Portugal): O meu relógio é novo.

Yes, it literally translates to "The my watch". In European Portuguese, we almost always put a definite article (o, a, os, as) before a possessive word like meu (my). Because relógio is a masculine noun, we use o meu.

Why do we use é (from the verb ser) instead of está (from estar) for "is"?

We use ser for permanent or defining characteristics. Even though a watch will not be new forever, being new or old is considered a core, classifying trait of the object, so we use é.

Does relógio mean watch or clock?

It means both! In Portuguese, the same word is used for a wristwatch, a wall clock, or a grandfather clock. The accent mark on the ó tells you to stress that syllable and give it an open sound.

Could I say O meu relógio é nova?

No, because relógio is a masculine noun. All the words describing it must match its gender, so you need the masculine adjective novo (new) instead of the feminine nova.