Learn Turkish: Birinci vagon bomboş. - The first carriage is completely empty.

boş means empty. bomboş is an intensive adjective meaning completely empty. Turkish forms these emphasis words by taking the first syllable or vowel sound of the adjective (here, bo-), adding an extra consonant (m, p, r, or s), and attaching it to the front of the word. Another common example is bembeyaz (completely white).

Why is the suffix -inci used on bir?

The suffix -inci (which adapts to 4-way vowel harmony as -ncı, -uncu, or -üncü) turns a standard number into an ordinal number, showing its position in a series. So bir (one) becomes birinci (first). If the base number already ends in a vowel, like iki (two), the suffix drops its initial vowel and attaches as just -nci (ikinci).

Where is the verb "is" in this sentence? Why isn't it bomboştur?

The "is" is implied. In everyday Turkish, the third-person "to be" suffix (like -tur or -tır) is frequently dropped in simple descriptions or statements of fact. You could absolutely say Birinci vagon bomboştur, but that sounds a bit more formal, written, or emphatic. Ending simply on bomboş is the most natural way to say this in daily life.