Learn Polish: Ten stary stół jest bardzo duży.

In Polish, adjectives change their endings to match the gender of the noun they describe. Because stół (table) is a masculine noun, the adjectives describing it get the standard masculine ending, which is usually -y (or sometimes -i).

How can I tell that stół is a masculine noun?

You can usually guess a noun's gender by looking at its last letter. Since stół ends in a consonant (the letter ł), it is masculine. Feminine nouns usually end in -a, and neuter nouns usually end in -o or -e.

Why do we use ten for "this" instead of ta or to?

Just like adjectives, the word for "this" has to match the gender of the noun. Ten is the masculine form to match the masculine noun stół. If it were a feminine noun, you would use ta, and for a neuter noun, you would use to.

Does the word bardzo change depending on the gender of the noun?

No, bardzo (very) is an adverb, not an adjective. Adverbs describe verbs or other adjectives, and they never change their endings. It stays exactly the same no matter what gender the noun is.