Learn Arabic (Modern Standard): الساحل مزدحم جدا اليوم.

It is an active participle from the Form VIII verb ازدحم (to become crowded). The root is ز-ح-م (z-h-m). Normally, Form VIII inserts a 't' sound after the first root letter, but because the first letter here is a ز (z), that inserted 't' changes into a د (d) to make pronunciation smoother.

Why doesn't مزدحم have the definite article ال to match الساحل?

This is how Arabic forms a full nominal (noun-based) sentence. The subject الساحل (the coast) is definite, but the predicate مزدحم (crowded) must be indefinite. This mismatch in definiteness is exactly how Arabic implies the word 'is'. If both words had ال, it would just be a fragment meaning 'the crowded coast'.

Why does جدا come after the adjective instead of before it like the English word 'very'?

The word جدا (very) is an adverb that intensifies the adjective. Unlike English, Arabic grammar strictly requires this specific word to be placed immediately after the adjective it modifies, never before it.

Does اليوم mean 'the day' or 'today' in this context?

It translates to 'today'. While يوم means 'a day', adding the definite article to make it اليوم (literally 'the day') turns it into an adverb of time that specifically means 'today'.